# Multiple choice questions, distributions and hypothesis test

1. A sample of 25 households in Prolific City revealed a mean of 7.5 residing members and a standard deviation of 3. If the mean household size for the nation is 4.2, what is the value of the test statistic?

a. 27.5

b. 5.5

c. 1.1

d. 0.55

2. A college baseball coach read in a sports magazine that the average fastball speed of all the pitchers who competed last year in the college world series was 90.4 mph. The 16 pitchers who tried out for the school's team this year averaged 88.2 mph, and the standard deviation was 3.4 mph. What is the value of the test statistic?

a. -25.9

b. -0.65

c. -2.59

d. 0.65

3. Two samples of shelled corn were taken from a bin and the weight of each kernel was measured and compared to the mean from last year's entire bin. The test statistic from the first sample was 1.8, the test statistic from the second sample was 2.5, and the research team was astonished to learn that the mean and standard deviation were identical for both samples. If the first sample was composed of 16 kernels, how many kernels were weighed on the second occasion?

a. 8

b. 12

c. 22

d. 31

4. Suppose the average watermelon contains 144.0 brown seeds. Farmer Brown just picked 25 ripe melons from the south side of his big garden and found that the average was 141.0 seeds and the standard deviation was 2.4 seeds. The same test statistic was obtained from another sample of 36 melons picked from the north side of the garden, but this time the standard deviation was 3.6 seeds. What was the average number of seeds in each watermelon picked from the north side?

a. 140.25

b. 140.40

c. 140.54

d. 141.75

5. If the two samples are dependent, their population means can still be compared using the ____________ statistic.

a. paired t

b. Z

c. F

d. chi-square

6. Sherry Weinstein, a buyer, has decided that she will spend an extra $7 per shirt for the next 10,000 T-shirts she buys for her chain of stores only if the vendor of the more expensive shirt can show conclusive evidence that its shirt can withstand at least 20 more times in the wash without fading. The vendor elected to set m1 as the mean number of washes without fading for the more expensive shirt. An appropriate null hypothesis for the vendor to test is:

a. H0: m1 - m2 £ 20.

b. H0: m1 - m2 < 20.

c. H0: m1 - m2 > 20.

d. H0: m1 - m2 £ 0.

7. The weekly sales (in thousands of dollars) the week before and the week after a new Internet sales location is installed are given in the following table for 8 different businesses.

Sales Before Sales After

27

35

22

13

45

55

60

18 32

36

23

12

48

57

58

30

The alternative hypothesis is HA: md > 0, where d = sales after - sales before. For level of significance 0.10, what is the critical value and the value of the test statistic?

a. 1.645 and 1.70

b. 1.70 and 1.645

c. 1.70 and 1.895

d. 1.895 and 1.70

8. A paired difference test is being conducted involving 19 pairs of observations. What is the number of degrees of freedom for the test statistic?

a. 18

b. 19

c. 37

d. 38

#### Solution Preview

The solutions to these problems are given below.

Statistics

1. A sample of 25 households in Prolific City revealed a mean of 7.5 residing members and a standard deviation of 3. If the mean household size for the nation is 4.2, what is the value of the test statistic?

a. 27.5

b. 5.5

c. 1.1

d. 0.55

Standard deviation of sample mean = 3/sqrt(25) where sqrt means square root of. This = 3/5 = 0.6

Test statistic = (7.5 - 4.2)/standard deviation = (7.5 - 4.2)/0.6 = 3.3/0.6 = 5.5

2. A college baseball coach read in a sports magazine that the average fastball speed of all the pitchers who competed last year in the college world series was 90.4 mph. The 16 pitchers who tried out for the school's team this year averaged 88.2 mph, and the standard deviation was 3.4 mph. What is the value of the test statistic?

a. -25.9

b. -0.65

c. -2.59

d. 0.65

Standard deviation of sample mean = 3.4/sqrt(16) = 3.4/4 = 0.85. Here sqrt means square root of.

Again, the test statistic statistic = (88.2 - 90.4)/0.85 = -2.59 nearly.

3. Two samples of shelled corn were taken from a bin and the weight of each kernel was measured and compared to the mean from last year's entire bin. The test statistic from the first sample was 1.8, the test statistic from the second sample was 2.5, and the research team was ...

#### Solution Summary

How to perform a t test?

How to test a hypothesis based on mean and standard deviation?