Question

Use the following information to answer items 16 - 20.

Joan has just moved into a new apartment and wants to purchase a new couch. To determine if there is a difference between the average prices of couches at two different stores, she collects the following data. Test the hypothesis that there is no difference in the average price. Use α = 0.05. Use an independent z-test and the p-value method

	Store 1	Store 2
Sample Mean	$650	$680
Population SD	$43	$52
Sample Size	42	45

16. State the hypothesis.

17. Compute the test statistic (using z test).

18. Using Table E, find the p-value for the test value in item 17.

19. Is the p-value less than the α = 0.05?

20. Fill in the blanks to complete the summary of the study.Based on the data collected at Store 1 and 2, the difference in couch prices________ statistically significant, z =______ , p =______.

Answer 1

Independent z-test.

1. Null and alternative hypothesis.

Claim: There is no difference between the average prices. That is

The null and alternative hypotheses are,

H₀: There is no difference between the average prices, that is  

H₁: There is a difference between the average prices, that is  

Population standard deviations are known, so z test statistics is used.

2. Test statistics:

The formula of z-test statistics is,

where,

n₁: first sample size = 42

n2: second sample size = 45

3. P-value

The alternative hypothesis contains not equal to sign, so the test is a two-tailed test.

The test statistics is negative and the test is a two-tailed test, so the formula of P-value is

P-value = 2 * P(Z < z test statistics) = 2 * P(Z < -2.94)

The probability using table E for z = -2.94 is 0.0016

P-value = 2 * 0.0016 = 0.0032

Yes, the p-value is less than alpha = 0.05

Decision rule: If P-value < alpha then reject the null hypothesis otherwise fail to reject the null hypothesis.

Here P-value < alpha, so reject the null hypothesis.

Based on the data collected at store 1 and store 2, the difference in couch prices is statistically significant,

z = -2.94, p = 0.0032