Leech therapy is used in traditional medicine for treating localized pain. In a double blind experiment on 50 patients with osteoarthritis of the knee, half are randomly selected to receive injections of leech saliva while the rest receive a placebo. Palin levels 7 days later among those receiving the saliva show a mean of 19.5, while the pain levels among those receiving the placebo show a mean of 25.6 (higher numbers indicate more pain). Partial calculator output is shown below.

Leech therapy is used in traditional medicine for treating localized pain. In a double blind experiment on 50 patients with osteoarthritis of the knee, half are randomly selected to receive injections of leech saliva while the rest receive a placebo. Palin levels 7 days later among those receiving the saliva show a mean of 19.5, while the pain levels among those receiving the placebo show a mean of 25.6 (higher numbers indicate more pain). Partial calculator output is shown below.

2-SampleTTest
µ1<µ2
t = -3.939503313
df = 43.43159286
x1 = 19.5
x2 = 25.6
Sx1 = 4.5
Sx2 = 6.3
n1 = 25
n2 = 25
Which of the following is a correct conclusion?


(A) After 7 days, the mean pain level with the leech treatment is significantly lower than the mean pain level with the placebo at the 0.01 significance level.
(B) After 7 days, the mean pain level with the leech treatment is significantly lower than the mean pain level with the placebo at the 0.05 significance level, but not at the 0.01 level.
(C) After 7 days, the mean pain level with the leech treatment is significantly lower than the mean pain level with the placebo at the 0.10 significance level, but not at the 0.05 level.
(D) After 7 days, the mean pain level with the leech treatment is not significantly lower than the mean pain level with the placebo at the 0.10 significance level.
(E) The proper test should be a one-sample t-test on a set of differences.

Answer: A

A random sample of 16 lightbulbs of one brand was selected to estimate the mean lifetime that brand of bulbs. The sample mean was 1,025 hours, with a standard deviation of 130 hours. Assuming that the lifetimes are approximately normally distributed, which of the following will give a 95 percent confidence interval to estimate the mean lifetime?

A random sample of 16 lightbulbs of one brand was selected to estimate the mean lifetime that brand of bulbs. The sample mean was 1,025 hours, with a standard deviation of 130 hours. Assuming that the lifetimes are approximately normally distributed, which of the following will give a 95 percent confidence interval to estimate the mean lifetime?

(A) 1,025 ± 1.96 (130/v16)
(B) 1,025 ± 1.96 (v30)
(C) 1,025 ± 2.12 (130/v16)
(D) 1,025 ± 2.13 (130/v16)
(E) 1,025 ± 2.13 (130/v15)

A company is interested in comparing the mean sales revenue per salesperson at two different locations. The manager takes a random sample of 10 salespersons from each location independently and records the sales revenue generated by each person during the last 4 weeks. He decides to use a t-test to compare the mean sales revenue at the two locations. Which of the following assumptions is necessary for the validity of the t-test?

A company is interested in comparing the mean sales revenue per salesperson at two different locations. The manager takes a random sample of 10 salespersons from each location independently and records the sales revenue generated by each person during the last 4 weeks. He decides to use a t-test to compare the mean sales revenue at the two locations. Which of the following assumptions is necessary for the validity of the t-test?

(A) The population standard deviation at both locations are equal.
(B) The population standard deviations at both locations are not equal.
(C) The population standard deviations at both locations are known.
(D) The population of the sales records at each location is normally distributed.
(E) The population of the difference in sales records computed by pairing one salesperson from each location is normally distributed.

Which of the following statements correctly describes the relation between a t distribution and a standard normal distribution?

Which of the following statements correctly describes the relation between a t distribution and a standard normal distribution?

(A) The standard normal distribution is centered at 0, whereas the t-distribution is centered at (n-1).
(B) As the sample size increases, the difference between the t-distribution and the standard normal distribution increases.
(C) The standard normal is just another name for the t-distribution.
(D) The standard normal distribution has a larger standard deviation than the t distribution.
(E) The t-distribution has a larger standard deviation than the standard normal distribution.

Researchers are concerned that the mean clutch size (number of eggs per nest) of robin's eggs in a particular forest has decreased from the mean of 4.8 eggs measured ten years ago. They plan to send out teams to locate and count the number of eggs in fifty different nests, and then perform a hypothesis test to determine if their concerns are well-founded. What is the most appropriate test to perform in this situation?

Researchers are concerned that the mean clutch size (number of eggs per nest) of robin's eggs in a particular forest has decreased from the mean of 4.8 eggs measured ten years ago. They plan to send out teams to locate and count the number of eggs in fifty different nests, and then perform a hypothesis test to determine if their concerns are well-founded. What is the most appropriate test to perform in this situation?

(A) A one-tailed t-test on one population mean.
(B) A one-tailed t-test on the difference between two independent population means.
(C) A one-tailed t-test on the mean difference between ordered pairs.
(D) A one-tailed z-test on a population proportion.
(E) A chi-squared test on independence between two variables.

A consumer awareness group has received several complaints that the price of asthma medicine has significantly increased in the recent years. Two years ago, the mean price for this medicine was estimated to be $78.00, and the price at different pharmacies was approximately normally distributed. The group decides to select 10 pharmacies at random and record the pice of the medicine at each of the pharmacies. Assuming a 5 percent level of significance, which of the following decision rules should be used to these the hypotheses below?

A consumer awareness group has received several complaints that the price of asthma medicine has significantly increased in the recent years. Two years ago, the mean price for this medicine was estimated to be $78.00, and the price at different pharmacies was approximately normally distributed. The group decides to select 10 pharmacies at random and record the pice of the medicine at each of the pharmacies. Assuming a 5 percent level of significance, which of the following decision rules should be used to these the hypotheses below?

Ho: The mean price of medicine is $78.00
Ha: The mean price of medicine is higher than $78.00


(A) Reject the null hypothesis if p-value > 0.05.
(B) Reject the null hypothesis if p-value > 0.025.
(C) Reject the null hypothesis if X > 78.00.
(D) Reject the null hypothesis if the test statistic > 1.812
(E) Reject the null hypothesis if the test statistic > 1.833

A farmer wants to know whether a new fertilizer has increased the mean weight of his apples With the old fertilizer, the mean weight was 4.0 ounces per apple. The farmer decides to test H0: µ = 4.0 ounces verses Ha: µ > 4.0 ounces, at a 5 percent level of significance, where µ is approximately normally distributed. The farmer takes a random sample of 16 apples and computes a mean of 4.3 ounces and a standard deviation of 0.6 ounces. Which of the following gives the p-value for the test?

A farmer wants to know whether a new fertilizer has increased the mean weight of his apples With the old fertilizer, the mean weight was 4.0 ounces per apple. The farmer decides to test H0: µ = 4.0 ounces verses Ha: µ > 4.0 ounces, at a 5 percent level of significance, where µ is approximately normally distributed. The farmer takes a random sample of 16 apples and computes a mean of 4.3 ounces and a standard deviation of 0.6 ounces. Which of the following gives the p-value for the test?

(A) P (Z > 2)
(B) P (Z < 2)
(C) P (t > 2) with 15 degrees of freedom
(D) P (t < 2) with 15 degrees of freedom
(E) P (t > 2) with 16 degrees of freedom

Does socioeconomic status relate to age at time of HIV infection? For 274 high-income HIV-positive individuals the average age of infection was 33.0 years with a standard deviation of 6.3, while for 90 low-income individuals the average age was 28.6 years with a standard deviation of 6.3 (The Lancet, October 22, 1994, page 1121). Find a 90% confidence interval estimate for the difference in ages of high-and low-income people at the time of HIV infection.

Does socioeconomic status relate to age at time of HIV infection? For 274 high-income HIV-positive individuals the average age of infection was 33.0 years with a standard deviation of 6.3, while for 90 low-income individuals the average age was 28.6 years with a standard deviation of 6.3 (The Lancet, October 22, 1994, page 1121). Find a 90% confidence interval estimate for the difference in ages of high-and low-income people at the time of HIV infection. 

(A) 4.4 +/- 0.963
(B) 4.4 +/- 1.26
(C) 4.4 +/- 2.51
(D) 30.8 +/- 2.51
(E) 30.8 +/- 6.3

Answer: B

An engineer wishes to determine the difference in life expectancies of two brands of batteries. Suppose the standard deviation of each brand is 4.5 hours. How large a sample (same number) of each type of battery should be taken if the engineer wishes to be 90% certain of knowing the difference in the life expectancies to within one hour?

An engineer wishes to determine the difference in life expectancies of two brands of batteries. Suppose the standard deviation of each brand is 4.5 hours. How large a sample (same number) of each type of battery should be taken if the engineer wishes to be 90% certain of knowing the difference in the life expectancies to within one hour?

(A) 10
(B) 55
(C) 110
(D) 156
(E) 202

Answer: C

A researcher believes a new diet should improve weight gain in laboratory mice. If ten control mice on the old diet gain an average of 4 ounces with a standard deviation of 0.3 ounces, while the average gain for ten mice on the new diet is 4.8 ounces with a standard deviation of 0.2 ounces, where is the p-value?

A researcher believes a new diet should improve weight gain in laboratory mice. If ten control mice on the old diet gain an average of 4 ounces with a standard deviation of 0.3 ounces, while the average gain for ten mice on the new diet is 4.8 ounces with a standard deviation of 0.2 ounces, where is the p-value?

(A) Below .01
(B) Between .01 and .025
(C) Between .025 and .05
(D) Between .05 and .10
(E) Over .10

Answer: A

The Department of Transportation of the State of New York claimed that it takes an average of 200 minutes to travel by train from New York to Buffalo. A random sample of 40 trains was taken and the average time required to travel from New York to Buffalo was 188 minutes, with a standard deviation of 28 minutes. What is the p-value for this test?

The Department of Transportation of the State of New York claimed that it takes an average of 200 minutes to travel by train from New York to Buffalo. A random sample of 40 trains was taken and the average time required to travel from New York to Buffalo was 188 minutes, with a standard deviation of 28 minutes. What is the p-value for this test? 

(A) .0355
(B) .0099
(C) .1294
(D) .2881
(E) .1167

Answer: B

The quality department of an electronics manufacturer randomly selected 100 resistors. The mean resistance of the resistors was 201.5O and the standard deviation was .4O. Find the 98% confidence interval for this problem.

The quality department of an electronics manufacturer randomly selected 100 resistors. The mean resistance of the resistors was 201.5O and the standard deviation was .4O. Find the 98% confidence interval for this problem.

(A) 201.5+/-.093
(B) 201.5+/-.125
(C) 201.5+/-.133
(D) 201.5+/-.155
(E) 201.5+/-.212

Answer: A

Which of the following is a criterion for choosing a t-test rather than a z-test when making an inference about the mean of a population?

Which of the following is a criterion for choosing a t-test rather than a z-test when making an inference about the mean of a population?

(A) The standard deviation of the population is unknown.
(B) The mean of the population is unknown.
(C) The sample may not have been a simple random sample.
(D) The population is not normally distributed.
(E) The sample size is less than 100.

Answer: A

A geologist claims that a particular rock formation will yield a mean amount of 24 pounds of chemical per ton of excavation. His company, fearful that the true amount will be less, plans to run a test on a random sample of 50 tons. They will reject the 24 pound claim if the sample mean is less than 22. Suppose the standard deviation between tons is 5.8 pounds. If the true mean is 20 pounds of chemical, what is the probability that the test will result in a failure to reject the incorrect 24 pound claim?

A geologist claims that a particular rock formation will yield a mean amount of 24 pounds of chemical per ton of excavation. His company, fearful that the true amount will be less, plans to run a test on a random sample of 50 tons. They will reject the 24 pound claim if the sample mean is less than 22. Suppose the standard deviation between tons is 5.8 pounds. If the true mean is 20 pounds of chemical, what is the probability that the test will result in a failure to reject the incorrect 24 pound claim?

(A) .0073
(B) .4927
(C) .5073
(D) .8200
(E) .9927

Answer: A

A factory manager claims that the plant's smokestacks spew forth only 350 pounds of pollution per day. A government investigator suspects that the true value is higher and plans a hypothesis test with a critical value of 375 pounds. Suppose the standard deviation in daily pollution poundage is 150 and the true mean is 385 pounds. If the sample size is 100 days, what is the probability that the investigator will mistakenly fail to reject the factory manager's false claim?

A factory manager claims that the plant's smokestacks spew forth only 350 pounds of pollution per day. A government investigator suspects that the true value is higher and plans a hypothesis test with a critical value of 375 pounds. Suppose the standard deviation in daily pollution poundage is 150 and the true mean is 385 pounds. If the sample size is 100 days, what is the probability that the investigator will mistakenly fail to reject the factory manager's false claim?

(A) .0475
(B) .2514
(C) .7486
(D) .7514
(E) .9525

Answer: B

In a study aimed at reducing developmental problems in low-birth-weight (under 2500 grams) babies (Journal of the American Medical Association, June 13, 1990, page 3040), 347 infants were exposed to a special educational curriculum while 561 did not receive any special help. After 3 years the children exposed to the special curriculum showed a mean IQ of 93.5 with a standard deviation of 19.1; the other children had a mean IQ of 84.5 with a standard deviation of 19.9. Find a 95% confidence interval estimate for the difference in mean IQs of low-birth-weight babies who receive special intervention and those who do not.

In a study aimed at reducing developmental problems in low-birth-weight (under 2500 grams) babies (Journal of the American Medical Association, June 13, 1990, page 3040), 347 infants were exposed to a special educational curriculum while 561 did not receive any special help. After 3 years the children exposed to the special curriculum showed a mean IQ of 93.5 with a standard deviation of 19.1; the other children had a mean IQ of 84.5 with a standard deviation of 19.9. Find a 95% confidence interval estimate for the difference in mean IQs of low-birth-weight babies who receive special intervention and those who do not.

(A) (93.5-84.5) ± 1.97 v((19.1)2/347)+((19.9)2/561))
(B) (93.5-84.5) ± 1.97 ((19.1/v347)+(19.9/v561))
(C) (93.5-84.5) ± 1.65 v((19.1)2/347)+((19.1)2/561))
(D) (93.5-84.5) ± 1.65 ((19.1/v347)+(19.9/v561))
(E) (93.5-84.5) ± 1.65 v((19.1)2+(19.9)2)/(347+561))

Answer: A

Under what conditions would it be meaningful to construct a confidence interval estimate when the data consist of the entire population?

Under what conditions would it be meaningful to construct a confidence interval estimate when the data consist of the entire population?

(A) If the population size is small (n < 30)
(B) If the population size is large (n = 30)
(C) If a higher level of confidence is desired.
(D) If the population is truly random.
(E) Never

Answer: E

A social scientist wishes to determine the differences between the percentage of Los Angeles marriages and percentage of New York marriages that end in divorce in the first year. How large a sample (same for each group) should be taken to estimate the difference to within ±.07 at the 94% confidence level?

A social scientist wishes to determine the differences between the percentage of Los Angeles marriages and percentage of New York marriages that end in divorce in the first year. How large a sample (same for each group) should be taken to estimate the difference to within ±.07 at the 94% confidence level?

(A) 181
(B) 361
(C) 722
(D) 1083
(E) 1443

Answer: C

What is the critical t-value for finding a 90% confidence interval estimate from a sample of 15 observations?

What is the critical t-value for finding a 90% confidence interval estimate from a sample of 15 observations?

(A) 1.341
(B) 1.345
(C) 1.350
(D) 1.753
(E) 1.761

Answer: A

Acute renal graft rejection can occur years after the graft. In one study (The Lancet, December 24, 1994, page 1737), 21 patients showed such late acute rejection when the ages of their grafts (in years) were 9, 2, 7, 1, 4, 7, 9, 2, 6, 2, 3, 7, 6, 2, 3, 1, 2, 3, 1, 1, 2, and 7, respectively. Establish a 90% confidence interval estimate for the ages of renal grafts that undergo late acute rejection.

Acute renal graft rejection can occur years after the graft. In one study (The Lancet, December 24, 1994, page 1737), 21 patients showed such late acute rejection when the ages of their grafts (in years) were 9, 2, 7, 1, 4, 7, 9, 2, 6, 2, 3, 7, 6, 2, 3, 1, 2, 3, 1, 1, 2, and 7, respectively. Establish a 90% confidence interval estimate for the ages of renal grafts that undergo late acute rejection.

(A) 2.024 ± 0.799
(B) 2.024 ± 1.725
(C) 4.048 ± 0.799
(D) 4.048 ± 1.041
(E) 4.048 ± 1.725

Answer: C

Nine subjects, 87 to 96 years old, were given 8 weeks of progressive resistance weight training (Journal of the American Medical Association, June 13, 1990, page 3032). Strength before and after training for each individual was measured as maximum weight (in kilograms) lifted by left knee extension:

Nine subjects, 87 to 96 years old, were given 8 weeks of progressive resistance weight training (Journal of the American Medical Association, June 13, 1990, page 3032). Strength before and after training for each individual was measured as maximum weight (in kilograms) lifted by left knee extension:

Before: ' 3' 3.5' 4' 6' 7' 8' 8.5' 12.5' 15
After: '' 7' 17' 19' 12' 19' 22' 28' 20' 28
Find a 95% confidence interval estimate for the strength gain.


(A) 11.61 ± 3.03
(B) 11.61 ± 3.69
(C) 11.61 ± 3.76
(D) 19.11 ± 1.25
(E) 19.11 ± 3.69

Answer: B

A catch of five fish of a certain species yielded the following ounces of protein per pound of fish: 3.1, 3.5, 3.2, 2.8, and 3.4. What is a 90% confidence interval estimate for ounces of protein per pound of this species of fish?

A catch of five fish of a certain species yielded the following ounces of protein per pound of fish: 3.1, 3.5, 3.2, 2.8, and 3.4. What is a 90% confidence interval estimate for ounces of protein per pound of this species of fish?

(A) 3.2 ± 0.202
(B) 3.2 ± 0.247
(C) 3.2 ± 0.261
(D) 4.0 ± 0.202
(E) 4.0 ± 0.247

Answer: A

An engineer wishes to determine the quantity of heat being generated by a particular electronic component. If she knows that the standard deviation is 2.4, how many of these components should she consider to be 99% sure of knowing the mean quantity to within ±0.6.

An engineer wishes to determine the quantity of heat being generated by a particular electronic component. If she knows that the standard deviation is 2.4, how many of these components should she consider to be 99% sure of knowing the mean quantity to within ±0.6.

(A) 27
(B) 87
(C) 107
(D) 212
(E) 425

Answer: C

The mean and standard deviation of the population {1, 5, 8, 11, 1} are µ = 8 and s = 4.8, respectively. Let S be the set of the 125 ordered triplets (repeats allowed) of elements of the original population. Which of the following is a correct statement about the mean µx and standard deviation sx of the means of the triplets in S?

The mean and standard deviation of the population {1, 5, 8, 11, 1} are µ = 8 and s = 4.8, respectively. Let S be the set of the 125 ordered triplets (repeats allowed) of elements of the original population. Which of the following is a correct statement about the mean µx and standard deviation sx of the means of the triplets in S?

(A) µx = 8, sx = 4.8
(B) µx = 8, sx < 4.8
(C) µx = 8, sx > 4.8
(D) µx < 8, sx = 4.8
(E) µx > 8, sx > 4.8

Answer: B

The 26 contestants in the pentathlon event of the 1992 Olympics ran the 200-mter dash in the following times (in seconds):

The 26 contestants in the pentathlon event of the 1992 Olympics ran the 200-mter dash in the following times (in seconds): 25.44, 24.39, 25.66, 23.93, 23.34, 25.01, 24.27, 24.54, 25.44, 24.86, 23.95, 23.31, 24.60, 23.12, 25.29, 24.40, 25.24, 24.43, 23.70, 25.20, 25.09, 24.48, 26.13, 25.28, 24.18, and 23.83. (Journal of the American Statistical Association, September 1994, page 1101). In testing the null hypothesis that the mean time required for pentathlon contestants to run this race is 25 seconds against the alternative hypothesis that the mean time required is less than 25 seconds, in which of the following intervals is the P-value located?

(A) P < .005
(B) .005 < P < .01
(C) .01 < P < .05
(D) .05 < P < .10
(E) .10 < P

Answer: B

An auditor remarks that the accounts receivable for a company seem to average about $2000. A quick check of 20 accounts gives a mean of $2250 with a standard deviation of $600. Where is the P-value?

An auditor remarks that the accounts receivable for a company seem to average about $2000. A quick check of 20 accounts gives a mean of $2250 with a standard deviation of $600. Where is the P-value?

(A) Below .01
(B) Between .01 and .025
(C) Between .025 and .05
(D) Between .05 and .10
(E) Over .10

Answer: D

A recent study of health service costs for coronary angioplasty versus coronary artery bypass surgery at a London hospital (The Lancet, October 1, 1994, page 929) showed an average cost of £6176 with a standard deviation of £329 for 231 angioplasties and an average cost of £8164 with a standard deviation of £264 for 221 bypass surgeries. Is this sufficient evidence to say that the average cost of angioplasty is less than the average cost of bypass surgery?

A recent study of health service costs for coronary angioplasty versus coronary artery bypass surgery at a London hospital (The Lancet, October 1, 1994, page 929) showed an average cost of £6176 with a standard deviation of £329 for 231 angioplasties and an average cost of £8164 with a standard deviation of £264 for 221 bypass surgeries. Is this sufficient evidence to say that the average cost of angioplasty is less than the average cost of bypass surgery?

(A) P < .001, so this is very strong evidence that angioplasty costs less.
(B) P is between .001 and .01, so this is strong evidence that angioplasty costs less.
(C) P is between .01 and .05, so this is moderate evidence that angioplasty costs less.
(D) P is between .05 and .10, so there is some evidence that angioplasty costs less.
(E) P > .10, so there is little evidence that angioplasty costs less.

Answer: A

A city spokesperson claims that the mean response time for arrival of a fire truck at a fire is 12 minutes. A newspaper reporter suspects that the response time is actually longer an runs a test by examining the records of 64 fire emergency situations. What conclusion is reached if the sample mean is 13.1 minutes with a standard deviation of 6 minutes?

A city spokesperson claims that the mean response time for arrival of a fire truck at a fire is 12 minutes. A newspaper reporter suspects that the response time is actually longer an runs a test by examining the records of 64 fire emergency situations. What conclusion is reached if the sample mean is 13.1 minutes with a standard deviation of 6 minutes?

(A) The P-value is less than .001, indicating very strong evidence agains the 12-minute claim.
(B) The P-value is .01, indicating strong evidence against the 12-minute claim.
(C) The P-value is .07, indicating some evidence against the 12-minute claim.
(D) The P-value is .18, indicating very little evidence against the 12-minute claim.
(E) The P-value is .43, indicating no evidence against the 12-minute claim.

Answer: C

An IRS representative claims that the average deduction for medical care is $1250. A taxpayer who believes that real figure is lower samples 12 families and comes up with a mean of $934 and a standard deviation of $616. Where is the P-value?

An IRS representative claims that the average deduction for medical care is $1250. A taxpayer who believes that real figure is lower samples 12 families and comes up with a mean of $934 and a standard deviation of $616. Where is the P-value?

(A) Below .01
(B) Between .01 and .025
(C) Between .025 and .05
(D) Between .05 and .10
(E) Over .10

Answer: D

In a one-sided hypothesis test for the mean, in a random sample of size 10 the tscore of the sample mean is 2.79. Is this significant at the 5% level? At the 1% level?

In a one-sided hypothesis test for the mean, in a random sample of size 10 the tscore of the sample mean is 2.79. Is this significant at the 5% level? At the 1% level?

(A) Significant at the 1% level but not at the 5% level.
(B) Significant at the 5% level but not at the 1% level.
(C) Significant at both the 1% and 5% levels.
(D) Significant at neither the 1% nor 5% level.
(E) Cannot be determined from the given information.

Answer: B

A team of biologists has collected date for an experiment on caloric intake of 28 lab rats. They used a one-sample t-test with a = 0.05 and chose to run a two-sided test. Which of the following is the smallest possible test statistic that would reject the null hypothesis in favor of the alternative hypothesis?

A team of biologists has collected date for an experiment on caloric intake of 28 lab rats. They used a one-sample t-test with a = 0.05 and chose to run a two-sided test. Which of the following is the smallest possible test statistic that would reject the null hypothesis in favor of the alternative hypothesis?

(A) 1.253
(B) 1.701
(C) 1.703
(D) 2.012
(E) 2.301

Answer: E

Twenty-six randomly selected packages of multicolored candies were opened and the number of blue candies in each recorded. The sample mean number of blue candies was 7, and the standard deviation was 1. Which of the following is a 90% confidence interval for the mean number of blue candies per package?

Twenty-six randomly selected packages of multicolored candies were opened and the number of blue candies in each recorded. The sample mean number of blue candies was 7, and the standard deviation was 1. Which of the following is a 90% confidence interval for the mean number of blue candies per package?

(A) 7 ± 1.706 (1/v26)
(B) 7± 1.708 (1/v25)
(C) 7 ± 1.708 (1/v26)
(D) 7 ± 1.2060 (1/v26)
(E) 7 ± 2.060 (1/v25)

Answer: C

In which of the following instances would the t-distribution be used to model the sampling distribution of a single sample statistic instead of the z-distribution?

In which of the following instances would the t-distribution be used to model the sampling distribution of a single sample statistic instead of the z-distribution?

(A) Constructing a confidence interval for the population proportion; the population proportion, p, is unknown.
(B) Conducting a matched-pairs hypothesis test for the population mean difference; the population standard deviation of the difference, sd, is known.
(C) Constructing a confidence interval for the difference between two population means; the population standard deviations, s1 and s2, are unknown.
(D) Conducting a hypothesis test for the difference between two population proportions; the population proportions p1 and p2, are unknown.
(E) Constructing a confidence interval for a population mean; the population standard deviation, s, is known.

Answer: C

The maker of printer cartridges for laser printers wants to estimate the mean number of documents µ that can be printed on a new high-speed printer. The company decides to test the cartridge on two dozen different laser printers. Each document is identical in number of words and amount of graphics. A histogram of the number of pages printed for each printer shows no outliers and is fairly bell-shaped. The mean and standard deviation of the sample were 3,875 sheets, and 170 sheets, respectively. It can be assumed that the laser printers were a random sample of all laser printers on the market. Which of the following is the correct formula for a 90% confidence interval for the mean number of pages printed with the new type of cartridge?

The maker of printer cartridges for laser printers wants to estimate the mean number of documents µ that can be printed on a new high-speed printer. The company decides to test the cartridge on two dozen different laser printers. Each document is identical in number of words and amount of graphics. A histogram of the number of pages printed for each printer shows no outliers and is fairly bell-shaped. The mean and standard deviation of the sample were 3,875 sheets, and 170 sheets, respectively. It can be assumed that the laser printers were a random sample of all laser printers on the market. Which of the following is the correct formula for a 90% confidence interval for the mean number of pages printed with the new type of cartridge?

(A) 3,875 ± 1.711 × (170/v24)
(B) 3,875 ± 1.714 × (170/v24)
(C) 3,875 ± 1.711 × (170/v23)
(D) 3,875 ± 1.714 × (170/v23)
(E) The company should only compute a 95% confidence interval for these data.

Answer: B

A light bulb manufacturer wishes to estimate the mean lifetime (in hours) of its new "long-life" bulb. Thirty bulbs were tested and the lifetime was recorded for each. The mean of the sample was 1,450 hours and the standard deviation of the sample was 150 hours. Assuming all conditions for inference are satisfied, what is the 99% confidence interval for µ, the mean lifetime of the new "long-life" bulb?

A light bulb manufacturer wishes to estimate the mean lifetime (in hours) of its new "long-life" bulb. Thirty bulbs were tested and the lifetime was recorded for each. The mean of the sample was 1,450 hours and the standard deviation of the sample was 150 hours. Assuming all conditions for inference are satisfied, what is the 99% confidence interval for µ, the mean lifetime of the new "long-life" bulb?

(A) 1450 ± 2.750(150/v30)
(B) 1450 ± 2.756(150/v30)
(C) 1450 ± 2.750(150/v29)
(D) 1450 ± 2.756(150/v29)
(E) 1450 ± 0.8389(150/v29)

Answer: B