To answer this question, use the Data Analysis Toolpack in Excel and select “t-T

Question

To answer this question, use the Data Analysis Toolpack in Excel and select “t-Test: Two-Sample Assuming Equal Variances” from the list of available tools. Conduct a hypothesis test using this tool. Explain your answer (how you decided if men spend more or not) and include the output table. Some studies have shown that in the United States, men spend more than women buying gifts and cards on Valentine’s Day. Suppose a researcher wants to test this hypothesis by randomly sampling 9 men and 10 women 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 1 month before Valentine’s Day and record all purchases made for Valentine’s Day during that 1-month period. The resulting data are shown below. Use these data and a 1% level of significance to test to determine if, on average, men actually do spend significantly more than women on Valentine’s Day. Assume that such spending is normally distributed in the population and that the population variances are equal. Make sure you clearly state both the null and the alternative hypotheses in full sentences. Include the output table; then, clearly state the conclusion in the same manner (do not simply say “accept/reject null”) and explain how you arrived at this conclusion (based on which metrics) Men Women 107.48 125.98 143.61 59.32 90.19 96.35 125.53 80.62 70.79 77.6 83 84.34 129.63 75.21 154.22 68.48 Null hypothesis: Alternative hypothesis: Calculated p or t value: Conclusion (justify using the metrics):

Explanation / Answer

The null hypothesis is : average spending of men is equal to that of women.
The alternative hypothesis is : average spending of men is greater to that of women.
Given, level of significance = 0.01
We paste the data in Excel and carry out the two sample t test to test these hypotheses, assuming equal variances.
Following is the result that we got in Excel.

From the output above, we see that the calculated p-value is 0.018407. Since the p-value is greater than 0.01 level of significance, we fail to reject the null hypothesis.

Conclusion : We conclude that there is not enough statistical evidence to support the fact that the average spending of men is greater to that of women.

t-Test: Two-Sample Assuming Equal Variances Men Women Mean 113.0563 83.4875 Variance 900.2919 413.2112 Observations 8 8 Pooled Variance 656.7516 Hypothesized Mean Difference 0 df 14 t Stat 2.30761 P(T<=t) one-tail 0.018407 t Critical one-tail 2.624494 P(T<=t) two-tail 0.036815 t Critical two-tail 2.976843

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