1.

(12 pts) The manufacturers of Ben & Jerry's Ice Cream would like to check the quality of their batches of Cherry Garcia, their most popular ice cream flavor. Since they have recently been receiving complaints from customers claiming that there aren't enough cherries in their pints of Cherry Garcia, the company would like to evaluate whether their recent batches contain fewer cherries than their known average 27 cherries. Below are the numbers of cherries the company has counted in 9 pints they have manufactured from their most recent batch. Test this hypothesis using an alpha level of .01.

x: {19, 24, 22, 20, 26, 26, 21, 28, 19}

a. (2 pts) What is the appropriate test?

b. (1 pt) State your null hypothesis:

c. (1 pt) State your alternative hypothesis.

d. (2 pts) Find the critical value:

e. (3 pts) Calculate the obtained statistic:

f.(2 pts) Make a decision:

g.(1 pt) What does your decision mean?

2.

(10 pts) For the following data:

Group 1

3

2

1

8

4

Group 2

5

9

8

12

9

Calculate the following:

a.SS₁

b.SS₂

c.SS_D

d.S_D

e.S_x1-x2

(12 pts) The average IQ is 100. Below is a sample of 8 left-handed individuals who have been given an IQ test. Test the hypothesis that left-handed individuals have different IQs than the average American. Use an alpha level of .01.

IQ

120

90

110

100

80

90

100

90

1.Find the critical value:

2.Calculate the obtained statistic:

An education researcher would like to test whether 2^nd graders retain or lose knowledge during the summer when they are presumably not in school. She asks nine 2^nd graders to take a comprehension exam at the end of the school year (May), and then asks those same students to come back after the summer (late August) to retake a different but equivalent exam, to see if their level of comprehension has changed. Using the data below, test this hypothesis using an alpha level of .05.

May

August

90

100

65

80

78

92

50

60

89

90

92

98

75

70

90

96

65

87

1. a.Find the critical value:
2. a.Calculate the obtained statistic:

Below is a set of exam 1 scores from our Statistics class. 7 of the scores come from females, and 7 come from males. Test the hypothesis that males and females scored differently on our first exam, using an alpha level of .05.

Male

Female

65

99

90

78

87

43

98

56

46

72

61

90

70

100

1. a.Find the critical value:
2. a.Calculate the obtained statistic: