In a Bank of America study on consumer spending, Collected data on the amounts p

Question

In a Bank of America study on consumer spending, Collected data on the amounts paid by credit cards in six Different categories: "transport", "supermarket", "dining out", expenses for Home", "home furnishings", "dress "and "fun". Suppose that c on Data of 30 credit cards are identified the annual amounts that are They spent in "supermarket" (population 1) and "dinner out" (population 2). TO From the differences, the sample mean of these was = $ 850 and the deviation Sample standard was sd = $ 1, 123. A) Give the 95% confidence interval of two tails for the Difference between the population means. B) Formulate the null and alternative hypotheses to prove that there is no difference Between the population mean of the "supermarket" expenses paid with Credit card and the population mean of expenses on "dining out" Paid by credit card. C) With 0.05 as level of significance, is the null hypothesis rejected or not? D) Is there any relation between a) and c)? Explain.

Explanation / Answer

SOLUTION:

A) Sample Mean (M):850

Sample Size (n):30

Standard Deviation (s):1123

Confidence Level: 95%

Calculation

M = 850

t = 1.96

sM = (11232/30) = 205.03

= M ± Z(sM)

= 850 ± 1.96*205.03

= 850 ± 401.85

M = 850, 95% CI [448.15, 1251.85].

You can be 95% confident that the population mean () falls between 448.15 and 1251.85.

B)

Null hypothesis:(which we want to disprove) There is difference Between the population mean of the supermarket expenses paid with Credit card and the population mean of expenses on dining out Paid by credit card.

Alternative hypothesis:(which we want to prove)There is no difference Between the population mean of the supermarket expenses paid with Credit card and the population mean of expenses on dining out Paid by credit card.

C)We reject the null hypothesis and accept the alternative hypothesis. The z score of 4.15 is within the rejection area. The 2 cutoff points are 1.96 and -1.96. Since 4.15 is outside of this interval, we reject the null hypothesis. We accept the alternative hypothesis.

D) yes their is relation between a) and C)  if your significance level is 0.05, the corresponding confidence level is 95%. If the P value is less than your significance (alpha) level, thehypothesis test is statistically significant. If theconfidence interval does not contain the nullhypothesis value, the results are statistically significant.

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