# statistics 1865112 2

26. Consider the hypothesis test given by

: 0.5

: 0.5

1

0

H p

H p

In a random sample of 225 subjects, the sample proportion is found to be pˆ 0.51.

(a) Determine the test statistic.

(b) Determine the P value for this test. Show all work; writing the correct P value,

without supporting work, will receive no credit.

(c) Is there sufficient evidence to justify the rejection of H0 at the 0.01 level?

Explain.

words. Each was asked to list as many of the words as he or she could remember both 1

hour and 24 hours later. The result is shown in the following table.

Number of Words Recalled

Subject 1 hour later 24 hours later

1 14 12

2 18 15

3 11 9

4 13 12

5 12 12

Is there evidence to suggest that the mean number of words recalled after 1 hour exceeds

the mean recall after 24 hours?

Assume we want to use a 0.01 significance level to test the claim.

(a) Identify the null hypothesis and the alternative hypothesis.

(b) Determine the test statistic.

(c) Determine the critical value.

(d) Is there sufficient evidence to support the claim that the mean number of words

recalled after 1 hour exceeds the mean recall after 24 hours?

Refer to the following data for Questions 28 and 29.

x 0 1 3 5

y 3 2 3 8

28. Find an equation of the least squares regression line. Show all work; writing the correct

equation, without supporting work, will receive no credit.

29. Based on the equation from # 28, what is the predicted value of y if x = 4? Show all work

and justify your answer.

30. The UMUC MiniMart sells four different types of teddy bears. The manager reports that the four types are equally popular. Suppose that a sample of 100 purchases yields observed counts 30, 24, 22, and 24 for types 1, 2, 3, and 4, respectively.

Type

1

2

3

4

Number

30

24

22

24

Assume we want to use a 0.10 significance level to test the claim that the four types are equally popular.

(a) Identify the null hypothesis and the alternative hypothesis.

(b) Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit.

(c) Determine the critical value. Show all work; writing the correct critical value, without supporting work, will receive no credit.

(d) Is there sufficient evidence to support the manager’s claim that the four types are equally popular? Justify your answer.