Question

A data set about speed dating includes​ "like" ratings of male dates made by the female dates. The summary statistics are nequals195​, x overbarequals6.85​, sequals2.18. Use a 0.10 significance level to test the claim that the population mean of such ratings is less than 7.00. Assume that a simple random sample has been selected. Identify the null and alternative​ hypotheses, test​ statistic, P-value, and state the final conclusion that addresses the original claim.

What are the null and alternative​ hypotheses?

A. Upper H 0​: muequals7.00 Upper H 1​: mugreater than7.00

B. Upper H 0​: muless than7.00 Upper H 1​: mugreater than7.00

C. Upper H 0​: muequals7.00 Upper H 1​: muless than7.00

D. Upper H 0​: muequals7.00 Upper H 1​: munot equals7.00

Determine the test statistic. nothing ​(Round to two decimal places as​ needed.)

Determine the​ P-value. nothing ​(Round to three decimal places as​ needed.)

State the final conclusion that addresses the original claim. ▼ Fail to reject Reject Upper H 0. There is ▼ sufficient not sufficient evidence to conclude that the mean of the population of ratings is ▼ less than not equal to greater than 7.00.

Answer 1

We have to test claim that the population mean of such ratings is less than 7.00

So, Ho: mean is equal to 7

Ha: mean is less than 7

option C is correct

test statistics t=

degree of freedom = n- 1= 195-1 = 194

using t distribution, check -0.96 in the left column and df(194) in row, we get

p value= 0.169

p value is more than 0.05 significance level, failed to reject the null hypothesis. We have insufficient evidence to claim that population mean of such ratings is less than 7.00

Fail to reject Upper H 0. There is not sufficient evidence to conclude that the mean of the population of ratings is less than 7.00.