Question

Some studies have shown that in the United States, the difference between men and women spending is less than $40 in buying gifts and cards on Valentine’s Day. Suppose a researcher wants to test this hypothesis by randomly sampling 10 women and 9 men with comparable demographic characteristics from various large cities across the United States to be in a study. Each study participant is asked to keep a log beginning one month before Valentine’s Day and record all purchases made for Valentine’s Day during that one-month period.

(1). The average of women and men spending are $75.48 and $110.92 respectively. The sample standard deviation of women and men are $30.51 and $28.79 respectively. Use 1% level of significance to manually determine if, on average, the difference between men and women spending is less than $40. Assume that such spending is normally distributed in the population and that the population variances are equal. What is the statistical decision and business decision?

(2). Import data VdaySpend_men and VdaySpend_women.csv. Write the correct R commands to determine on average, the difference between men and women spending is less than $40 on Valentine’s Day. Use 1% level of significance (alpha = 0.01). What is the p value? What is the statistical decision?

(3). Using the same data, write the correct R command to compute the confidence interval at 90% confidence level of the difference in spending of men and women on Valentine’s Day.

men

107.48

143.61

90.19

125.53

70.79

83

129.63

154.22

93.8

women

125.98

45.53

56.35

80.62

46.37

44.34

75.21

68.48

85.84

126.11

Answer 1

(c)

R-code:

m=c(107.48,143.61,90.19,125.53,70.79,83,129.63,154.22,93.8)
w=c(125.98,45.53,56.35,80.62,46.37,44.34,75.21,68.48,85.84,126.11)
#90% confidence level of the difference in spending of men and women on Valentine’s Day.
t.test(m,w,conf.level = 0.90)

R-console :

> m=c(107.48,143.61,90.19,125.53,70.79,83,129.63,154.22,93.8)

> w=c(125.98,45.53,56.35,80.62,46.37,44.34,75.21,68.48,85.84,126.11)

> #90% confidence level of the difference in spending of men and women on Valentine’s Day.

> t.test(m,w,conf.level = 0.90)

Welch Two Sample t-test

data: m and w

t = 2.6039, df = 16.951, p-value = 0.01856

alternative hypothesis: true difference in means is not equal to 0

90 percent confidence interval:

11.75711 59.11023

sample estimates:

mean of x mean of y

110.9167 75.4830