Question

In: Statistics and Probability

DATA: Spending by Men Spending by Women 85 90 102 79 139 71 90 119 89...

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

129

119

101

110

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.

Solutions

Expert Solution

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.

orchestra answered 1 year ago

Next > < Previous

Related Solutions

DATA: Spending by Men Spending by Women 85 90 102 79 139 71 90 119 89...

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...

57, 69, 70, 71, 74, 77, 79, 80, 80, 80, 80, 81, 81, 82, 85, 85,...

57, 69, 70, 71, 74, 77, 79, 80, 80, 80, 80, 81, 81, 82, 85, 85, 86, 88, 91, 95, 95, 100 1) Create a relative frequency table for these data. 2) Create a histogram for these data and comment on the shape of the distribution (skewed, symmetric, etc). 3) Create a boxplot for the data (you’ll need to report the median, quartiles, and outliers).

In a population of 158 people: 85 men and 73 women, it was found that 60...

In a population of 158 people: 85 men and 73 women, it was found that 60 men and 46 women had health insurance, the rest no. 40 of the men with health insurance and 9 of the men without insurance, visited the MD office more than 5 times last year. In the other hand, 35 of the women with insurance and 8 of the women without insurance, visited the MD office more than 5 times last year. Giving this information,...

z = [ 100 93 90 89 80 79 78 75 67 60 45 42 41...

z = [ 100 93 90 89 80 79 78 75 67 60 45 42 41 40 30 20 15 12 10 9 2 1] Using MATLAB, Write fully vectorized code (no loops) to find index number of which the numbers have decreased by 40. Print results to command window.

85 1,810 90 4,825 79 438 82 775 84 1,213 96 8,692 88 2,356 76 266...

85 1,810 90 4,825 79 438 82 775 84 1,213 96 8,692 88 2,356 76 266 93 4,930 97 9,138 89 2,714 83 1,082 85 1,290 90 3,970 82 894 91 2,906 90 4,615 84 1,168 79 462 81 1,018 95 5,950 What is multiple R, R square, & Adjusted R square? Do regression model results indicate significance, meaning the results can be accepted? Yes or No. For every 1 increase in Temperature, how much do sales increase?

Construct a frequency polygon for the following: 60-69 12 70-79 15 80-89 10 90-99 2 100-109...

Construct a frequency polygon for the following: 60-69 12 70-79 15 80-89 10 90-99 2 100-109 1 110-119 0 120-129 1

Name MidtermScore FinalExamScore John 71 78 Leon 78 84 Mary 85 90 Alice 80 92 Juan...

Name MidtermScore FinalExamScore John 71 78 Leon 78 84 Mary 85 90 Alice 80 92 Juan 72 87 Abdul 81 86 Fay 79 79 Raymnd 85 89 Felix 83 87 Beth 91 95 Tasha 84 87 Emily 70 74 Doris 84 88 Xao 83 96 1. Use ggplot R coding to create a scatterplot in order to investigate if there is a linear relationship between MidtermScore and FinalExamScore. Let MidtermScore be designated x and FinalExamScore be designated y. 2. Use...

a study was done on the type of automobiles owned by women and men the data...

a study was done on the type of automobiles owned by women and men the data are shown at a=0.10 is there a relationship between the type of automobile owned and the gender of the individual men luxury 15, latge 9, middize 49, small 27 women 9, large 6 midsize 62,small 14 women

- To compare the proportions p1, p2 of men and women, respectively, who watch football data...

- To compare the proportions p1, p2 of men and women, respectively, who watch football data was collected. In a sample of 227 men, 106 said that they watch football, and in a sample of 156 women, 48 said they watch football. (These are not real data.) Compute a 97 percent confidence interval for the difference p1 − p2 of proportions. Give the Margin of Error E, Left end point and Right end point MOE = E = LEP =...

The data below shows the life expectancy of men and women in different countries: LifeExpMale LifeExpFemale...

The data below shows the life expectancy of men and women in different countries: LifeExpMale LifeExpFemale Argentina 74 67 Bangladesh 53 54 Brazil 68 62 Canada 80 73 China 72 68 Colombia 74 68 Egypt 61 60 Ethiopia 53 50 France 82 74 Germany 79 73 India 58 57 Indonesia 63 59 Iran 65 64 Italy 82 75 Japan 82 76 Kenya 63 59 Korea.North 73 67 Korea.South 73 67 Mexico 76 68 Morocco 66 63 Burma 56 53 Pakistan...

Subjects