Question

Walmart has an interest in monitoring the average back-to-school spending for grade-school students year to year. Every year the back-to-school spending data is published by the National Retail Federation. The following table shows the average back-to-school spending of households randomly sampled in 2016 and 2017 along with the population standard deviations and sample sizes for each sample. 2016 2017 Sample mean $606.40 $655.27 Sample size 35 38 Population standard deviation $160 $173 a. State the correct null and alternative hypotheses. b. Perform a hypothesis test using α = 0.10 to determine if the average household back-to-school spending in 2016 was different than it was in 2017. c. Use Confidence Interval to test this hypotheses

Answer 1

We are testing if there is a difference between two population means. We have been given the population Sd , so we will use z-test / normal dist test.

Since we are checking for difference on either sides, it is two tailed test.

In test stat the null difference = =0

a. State the correct null and alternative hypotheses.

Null: The mean spendings of 2016 and 2017 are same .

Alternative:The mean spendings of 2016 and 2017 are different.

b. Perform a hypothesis test using α = 0.10 to determine if the average household back-to-school spending in 2016 was different than it was in 2017.

	2016 (1)	2017 (2)
n	35	38
sample mean	606.4	655.27
pop SD	160	173
pop Var	25600	29929
Test Stat	-1.25389
α = 0.10
C.V.
C.V. at 5%
	1.644854	found using normal % dist tables
Criteria	Reject null if |Test stat| > C.V.
Decision	Fail to reject the null hypothesis at 10%.
	There is insufficient evidence to conclude that average spending was different for 2016 and 2017.

c. Use Confidence Interval to test this hypotheses

Again for this we will use 2-sided inteval where

(1 - α) confidence interval for population difference of mean

α = 0.10

So the critical value will remain the same. Substituting we have

Since the interval does include null difference '0', we fail to reject the null hypothesis. This is same as test because the level was same.