Question

You are doing some research on the cost of one-bedroom apartments in town. Based on prices from previous years, a real estate agent gives you the information that σ is approximately $55 and μ is approximately $675per month. Assume that price follows roughly a normal distribution. You have randomly selected 25 apartments for which the price was published. The average price for these apartments is ?̅=695. You are to test if μ is less than 675.You set the null and alternative hypotheses as follows:

?0: ?≤ 675 ?? ??: ?>675

a. Compute the test statistic value.

b. If α=0.05, what is the critical value?

c. What is the p value?

d. What is the conclusion if α=0.05?

e. What is the conclusion if α=0.02?

Answer 1

Result:

You are doing some research on the cost of one-bedroom apartments in town. Based on prices from previous years, a real estate agent gives you the information that σ is approximately $55 and μ is approximately $675per month. Assume that price follows roughly a normal distribution. You have randomly selected 25 apartments for which the price was published. The average price for these apartments is ?̅=695. You are to test if μ is less than 675.You set the null and alternative hypotheses as follows:

?0: ?≤ 675 ?? ??: ?>675

( note: there is difference in the problem given(to test if μ is less than 675, in this case ??: ?< 675) and the stated alternate hypothesis. We do the problem with the stated alternate hypothesis, ??: ?>675)

a. Compute the test statistic value.

z =1.8182

b. If α=0.05, what is the critical value?

Critical value = 1.645

c. What is the p value?

P value =0.0345

d. What is the conclusion if α=0.05?

Since p value 0.0345 is < 0.05 level of significance, Ho is rejected. We conclude that μ is greater than 675.

e. What is the conclusion if α=0.02?

Since p value 0.0345 is > 0.02 level of significance, Ho is not rejected. There is not enough evidence to conclude that μ is greater than 675.

Z Test of Hypothesis for the Mean
Data
Null Hypothesis                       m=	675
Level of Significance	0.05
Population Standard Deviation	55
Sample Size	25
Sample Mean	695
Intermediate Calculations
Standard Error of the Mean	11.0000
Z Test Statistic	1.8182
Upper-Tail Test
Upper Critical Value	1.645
p-Value	0.0345
Reject the null hypothesis