A certain population follows a Normal distribution with mean µ and standard deviation σ= 22.1. You collect data on four members of the population and test the hypothesis H₀: µ= 100; Ha: µ>100. You obtain a P-value of 0.052. Which of the following is true?

A certain population follows a Normal distribution with mean µ and standard deviation σ= 22.1. You collect data on four members of the population and test the hypothesis
H₀: µ= 100; Ha: µ>100.
You obtain a P-value of 0.052. Which of the following is true? 

A. There is some evidence against H₀, and a study using a larger sample size may be worthwhile.
B. This should be viewed as a pilot study, and the data suggest that further investigation of the hypotheses will not be fruitful at the 5% significance level.
C. At the 5% significance level, you have proved that H₀ is true.
D. You have failed to obtain any evidence for Ha.
E. None of the above.



Answer: A

We want to test H₀: µ= 1.5 vs. Ha: µ≠ 1.5 at α= .05. A 95% confidence interval for µ calculated from a given random sample is (1.4, 3.6). Based on this finding we

We want to test H₀: µ= 1.5 vs. Ha: µ≠ 1.5 at α= .05. A 95% confidence interval for µ calculated from a given random sample is (1.4, 3.6). Based on this finding we 

A. Cannot make any decision at all because the distribution of the population is unknown.
B. Fail to reject H₀.
C. Reject H₀.
D. Cannot make any decision at all because the value of the test statistic
E. Cannot make any decision at all because (1.4, 3.6) is only a 95% confidence interval for µ.



Answer: B

Which of the following is not a required condition for performing a z test about an unknown population mean µ?

Which of the following is not a required condition for performing a z test about an unknown population mean µ?

A. The data represent n independent observations.
B. The population distribution is Normal or the sample size is large (say n>30).
C. The data can be viewed as a simple random sample from the population of interest.
D. The population standard deviation is known.
E. np≥10 and nq≥10.




Answer: E

A researcher wishes to determine if students are able to complete a certain pencil and paper maze more quickly while listening to classical music. Suppose the time (in seconds) needed for high school students to complete the maze while listening to classical music follows a Normal distribution with mean µ and standard deviation σ= 4. Suppose that also, that in the general population of all high school students, the time needed to complete the maze follows a Normal distribution with mean 40 and standard deviation σ= 4. The researcher, therefore, decides to test the hypotheses H₀: µ= 40, Ha: µ< 40 To do so, the researcher has 10,000 high school students complete the maze with classical music playing. The mean time for these students is x-bar= 39.8 seconds. It is appropriate to conclude which of the following?

A researcher wishes to determine if students are able to complete a certain pencil and paper maze more quickly while listening to classical music. Suppose the time (in seconds) needed for high school students to complete the maze while listening to classical music follows a Normal distribution with mean µ and standard deviation σ= 4. Suppose that also, that in the general population of all high school students, the time needed to complete the maze follows a Normal distribution with mean 40 and standard deviation σ= 4. The researcher, therefore, decides to test the hypotheses
H₀: µ= 40, Ha: µ< 40
To do so, the researcher has 10,000 high school students complete the maze with classical music playing. The mean time for these students is x-bar= 39.8 seconds. It is appropriate to conclude which of the following? 

A. The researcher has proved that, for high school students, listening to classical music substantially improves the time it takes to complete the maze.
B. Although the researcher has obtained a statistically significant result, it has little practical significance.
C. The researcher has moderate evidence that, for high school students, listening to classical music substantially improves the time it takes to complete the maze.
D. The researcher has strong evidence that, for high school students, listening to classical music substantially improves the time it takes to complete the maze.
E. None of the above.


Answer: B

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)


Answer: ...

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.


Answer: ...

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



Answer: ...