Question

DATA:

Spending by Men Spending by Women

85 90

102 79

139 71

90 119

89 90

52 180

49 88

140 56

90 110

64 82

96 64

132 129

117 28

88 13

92 140

105 62

95 32

119 220

118 72

124 90

131 80

113 56

124 82

71 56

115 88

95 104

102 54

94 108

111 86

85 88

87 38

92 66

92 100

72 57

97 59

83 89

118 95

108 37

104 86

110 62

66

129

119

76

75

101

85

68

67

36

90

99

64

54

86

79

82

65

110  

69

A consumer research firm believe that men and women shop at malls for different reasons, and spend different amounts of money when they shop. While women shop more frequently and for longer amounts of time, men shop less frequently, but tend to spend more each time when they do shop. The research firm has collected spending data for 40 men and 60 women at a local mall and wish to analyze if men spend more when they shop then women based on this data.

NOTE: For this data set, we are assuming UNEQUAL VARIANCES.

a. Specify the competing Null and Alternate hypotheses that you will use to test the economist’s claim.

Null Hypothesis:

Alternative Hypothesis:

b. Is this a one-tailed test or a two-tailed test? Explain why.

Is this test of “independent samples” or “dependent samples”? Explain why.

c. Calculate the value of the t statistic and the appropriate p-value. Provide mean values, and provide the values for the following variables from the output: Mean Spending by Men: Mean Spending by Women: Test Statistic: p-value:

d. At the 99% confidence level (alpha = 0.01), does the data support the researchers claim? Explain how you came to this conclusion.

Answer 1

a.

Null hypothesis H0: Men shop for amount less than or equal to women.

Alternate hypothesis HA: Men shop for amount more than women.

b. This is a one-tailed test. We are only going to test if men shop for more amount than women or not. Hence, only one side of the probability curve is being tested.

This is a test of independent samples. This is because no person is in both the samples. Hence, one person cannot directly affect both the samples.

c. The sample mean and standard deviations are:

We calculate the t-statistic as:

The degree of freedom is calculated as:

The corresponding p-value for 98 DOF is close to 0.998.

d. As the p-value of 0.998 corresponds to a significance level of 1-0.998 = 0.002, we see that this is less than the significance level of 0.01. This means that the null hypothesis is rejected and the alternate hypothesis is accepted.

As the researcher is supporting the alternate hypothesis, the data supports the researchers claim.