# MCQs: Hypothesis Testing

1) A hypothesis test that involves a small sample requires that we make the following assumption that

A. a larger computed value of t will be needed to reject the null hypothesis

B. the confidence interval will be wider than for large samples

C. the region of acceptance will be wider than for large samples

D. the population is normally distributed

2) The area of rejection, on a bell shaped curve, defines the location of all those values that are

A. within the selected confidence interval for the test

B. so small or so large that the probability of their occurrence under a true null hypothesis is to be expected

C. so small or so large that the probability of their occurrence under a false null hypothesis is rather remote

D. so small or so large that the probability of their occurrence under a true null hypothesis is rather slim

3) What is the critical value for a two-tail, one sample hypothesis test in which a null hypothesis is tested at the 5% level of significance based on a sample size of 23?

A. 2.069

B. 1.717

C. 2.074

D. 1.714

4) A statistician was setting up a hypothesis test with a level of significance dictated by upper management. However, she was concerned that the test she wished to perform might have unacceptable large possibilities of Type II error, ß. Which of the following would solve this problem?

A. Convince upper management to use a larger p-value.

B. Convince upper management to use a smaller p-value.

C. Convince upper management to use a larger sample.

D. Convince upper management to reduce the level of significance of the test.

5) In classical hypothesis testing, the test statistic is to the critical value what the ________________.

A. p-value is to alpha

B. test statistic is to the p-value

C. critical value is to alpha

D. level of significance is to the test statistic

6) Doi Winery has two wine shops in the neighboring towns of Seamen and Batavia. The favorite wine, as advertised, is Raspberry wine. A survey of 300 customers at the Seamen store revealed that 225 individuals preferred the Raspberry wine while 290 out of 400 in Batavia preferred the same flavor. To test the hypothesis that there was no difference in preferences in the two towns, what is the alternate hypothesis?

A. µ1 < µ2

B. µ1 = µ2

C. µ1 > µ2

D. µ1 ≠ µ2

7) You are conducting a two-tailed test of means but your software package only calculates a one-tailed p-value equal to 0.13. The actual p-value for your test is

A. 0.13

B. 0.26

C. 0.065

D. need a table to calculate this value.

8) Cake manufacturer Little Diva's wants to increase the shelf life of its easy-to-fix cupcake mixes. Company's records indicate that the average shelf life of the mix is 230 days. A new, improved cupcake mix was developed and a sample of 10 boxes of the cupcake mix had these shelf lives (in days): 231, 233, 232, 233, 228, 231, 234, 229, 235, and 232. If the standard deviation was .67 and at the 0.025 significant level, has the shelf life of the cupcake mix increased?

A. Yes, because computed t is greater than the critical value.

B.No, because computed t lies in the region of acceptance.

C. Yes, because computed t is less than the critical value.

D. No, because 231.8 is quite close to 230.

9) A machine is set to fill the small size packages of Good and Better candies are packaged with 60 pieces of candies in each bag. Sampling results revealed: 3 bags of 61, 2 bags of 59, 1 bag of 58, and 2 bags of 62. How many degrees of freedom are there?

A. 9

B. 8

C. 1

D. 7

10) In a test for the equality of two variances (two-tailed), when the populations are normal, a 5% level of significance was used. Sample sizes were n1 = 13 and n2 = 10. The upper critical value for the test is

A. =FINV(0.05, 12, 9).

B. =FINV(0.025, 13, 10).

C. =FINV(0.025, 12, 9).

D. =FINV(1-0.025, 13, 10).

11) Flash Jolt, a manufacturer of camera equipment, annually introduces new models in the fall of the year. At the conclusion of the Christmas season, retail dealers are contacted regarding their stock on hand of each piece of equipment. It has been discovered that unless 47% of the new equipment ordered by the retailers in the fall had been sold by Christmas, immediate production cutbacks are needed. At the end of the 2009 Christmas shopping season a survey of 100 dealers indicated that 45% of Flash Jolt equipment had been sold. It was decided to continue production levels at the current levels. The statistical test was conducted at the 0.05 level. Computed z = -0.40.

A. Wrong decision, should have cut back production

B. Correct decision, not a significant difference

C. Cannot determine based on information given

D. The two percentage points be attributed to sampling error

12) A recent study by College Stat Company reported a nationwide survey of college students determined that students spend 2 hours studying for each hour in the classroom. Professor Baker at State College wants to determine whether the time students spend at her college is significantly different from the national average of 2 hours. A random sample of 20 statistics students resulted in an average of 1.75 hours with a standard deviation of 0.24 hours. A t-test was conducted at the 5% level of significance. The calculated value of t was -4.03. What was Professor Baker decision?

A. Cannot make a decision at this time; more data is required.

B. Fail to reject the null hypothesis.

C.Reject the null hypothesis, the test statistic exceeds the critical value.

D. Reject the alternative hypothesis statement.

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#### Solution Summary

The solution provides answers to multiple choice questions on hypothesis testing. Relevant workings are also included.