1) (Chapter 10) Given the following t-statistics (23 ...



Midterm—Sample Economics 173 Name_____________

Fall 2001 Instructor: Petry SSN______________

1. Given the following t-statistics (23 degrees of freedom) and p-values (1 tailed);

t-statistic: 1.7 ( p-value .05

t-statistic: 1.2 ( p-value .121

t-statistic: 2.1 ( p-value .023

What is the p-value for the t-statistic 1.3?

a. .141

b. .103

c. .042

d. .013

e. .461

2. When comparing the proportions of two populations, what type of test statistic is used?

a. z

b. t

c. F

d. all of the above

e. none of the above

3. Given a population standard deviation of 13, a sample mean of 40, and a confidence interval width of 10, and a critical value of 1.645, what is the sample size?

a. 4

b. 5

c. 6

d. 7

e. 8

4. If the p-value for a test is .4 then your decision is:

a. there is sufficient evidence to conclude the alternative is correct.

b. there is sufficient evidence to conclude the null is correct.

c. there is insufficient evidence to conclude the alternative is correct.

d. there is insufficient evidence to conclude neither is correct.

e. none of the above

5. Which of the following statements are equivalent?

I. Alpha

II. Beta

III. Probability of a Type I error

IV. Probability of a Type II error

V. Probability of Rejecting a true null

a. I and IV

b. I and III

c. I and III and V

d. II and V

e. II and IV and V

6. The 95% confidence interval for the population average final exam score is [126.4, 195.5]. To test the claim that the average final exam score of the population is 180 at a 3% level of significance, what will be your decision?

a. reject the null – conclude it is not 180

b. fail to reject the null – insufficient evidence to conclude it is not 180

c. reject the null – conclude it is 180

d. fail to reject the null – sufficient evidence to conclude it is not 180

e. cannot decide based on the given information

7. When doing a matched pairs test with differences distributed normally and unknown population standard deviation, which is the correct test statistic?

a. equal variances pooled t test for means

b. unequal variances pooled t test for means

c. single population means test on the difference

d. none of the above

e. any of the above will work

8. If you wish to know if more than 45% of the class scored above 70% on the exam, what is your null hypothosis?

a. H0: p=0.7

b. H0: p=0.45

c. H0: p>0.7

d. H0: p>0.45

e. any of the above will work

9. Suppose we are interested in whether the mean scores on the midterm for Economics 173 is below 80%. Given a p-value of .11 what is your conclusion?

a. fail to reject the null at any reasonable level of significance

b. cannot determine based on the given information

c. reject the null at any reasonable level of significance

d. fail to reject the null only if the significance level is .01

e. reject the null only if the significance level is .01

10. Given the following list of observations: 1, 10, 34, 15, 8, 40, 90, 41, 5, 16. What proportion is above 8?

a. .4

b. .5

c. .6

d. .7

e. .8

11. Before running an equal variances pooled t-test, what test should you run to formally decide if the needed assumptions are correct?

a. F-test for variances

b. t-test for variances

c. z-test for variances

d. no need to run a test

e. eyeball test

12. A pharmaceutical company currently produces an anesthetic whose effective time is normally distributed with mean 7.4 and standard deviation 1.2. It is considering the launch of a new drug that they believe has a lower mean effective time but the same standard deviation. In a clinical study meant to test their belief, what would be the appropriate null and alternative hypothesis?

a. Ho: ( > = 7.4, H1: ( < 7.4

b. Ho: ( > 7.4, H1: ( < =7.4

c. Ho: ( = 7.4, H1: ( ( 7.4

d. Ho: ( < = 7.4, H1: ( > 7.4

13. Irrespective of your answer in the last question suppose that you intend to do a two-sided test. You collect a sample and compute the sample mean. In order to reject the null hypothesis at a 10% level of significance, using a Z statistic of 1.645, and a sample size of 25,

a. you need the sample mean to be smaller than 7.01

b. you need the sample mean to be greater than 7.79

c. both of the above

d. none of the above

14. The mean of a sample is computed to be –0.301. It has been found out that the p-value is 0.275 when testing Ho: ( = 0 against the two sided alternative H1: ( ( 0. To test Ho: ( = 0 against the one sided alternative H1: ( < 0 at a significance level of 0.5, we will have:

a. a p-value of 0.275 and therefore reject the null hypothesis

b. a p-value of 0.138 and therefore reject the null hypothesis

c. a p-value of 0.862 and therefore accept the null hypothesis

d. a p-value of 0.5 and therefore the test results will be inconclusive.

15. The following table presents the summary statistics from a sample of 24 exam scores, expressed in percentages.

|Score |

| | |

|Mean |75.66667 |

|Standard Error |1.782226 |

|Median |73 |

|Mode |73 |

|Standard Deviation |8.731087 |

|Sample Variance |76.23188 |

|Kurtosis |0.646501 |

|Skewness |1.303676 |

|Range |30 |

|Minimum |66 |

|Maximum |96 |

|Sum |1816 |

|Count |24 |

|Confidence Level(95.0%) |3.68681 |

In order to do a test where the null hypothesis specifies the population mean to be equal to 70,

a. the t-distribution should be used to get a test statistic equal to 3.18

b. the z-distribution should be used to get a test statistic equal to 3.18

c. not enough information is given to calculate the test statistic

d. a pooled variance t-test should be used

16. Based on a 95 % confidence interval, if you tested Ho: ( = 70, H1: ( ( 70, you would:

a. not be able construct the confidence interval due to lack of information.

b. Accept the null hypothesis

c. Reject the null hypothesis

d. Reformulate a one sided hypothesis instead.

17. The pooled variance t-test is based on the following assumption(s):

a. that the two populations be independent

b. that the two populations have approximately equal variances

c. that both populations be normal

d. all of the above

18. A truck manufacturer has two plants, one in Champaign and one in Urbana. The CEO of this company suspects that the Urbana plant is more efficient (in terms of number of trucks produced each month) than the Champaign one. Let Champaign be plant 1 and Urbana be plant 2 . Then the test should be specified as:

a. H0: (1-(2 = 0, H1: (1-(2 ( 0

b. H0: (1-(2 = 0, H1: (1-(2 < 0

c. H0: (1-(2 = 0, H1: (1-(2 > 0

d. H0: (1-(2 < 0, H1: (1-(2 > 0

19. For the scenario described above, monthly production data was collected from both plants for a year and a pooled variance t-test was performed at the 5% significance level. The results of the test are presented below.

|  |CHAMPAIGN |URBANA |

|Mean |57.75 |55.66667 |

|Variance |5.840909091 |13.15152 |

|Observations |12 |12 |

|Pooled Variance |9.496212121 | |

|Hypothesized Mean Difference |0 | |

|df |22 | |

|t Stat |1.655995622 | |

|P(T ................
................

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