Question

A data set about speed dating includes​ "like" ratings of male dates made by the female dates. The summary statistics are

n=185​,

x=6.89​,

s=2.11.

Use a 0.05 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.

H0​: μ=7.00

H1​: μ<7.00

B. H0​: μ<7.00

H1​: μ>7.00

C.

H0​: μ=7.00

H1​: μ>7.00

D. H0​: μ=7.00

H1​: μ≠ 7.00

B. Determine the test statistic

C. Determine the P-Value

Answer 1

Solution :

Given that,

This is a left (One) tailed test,

The null and alternative hypothesis is,  

A)

Ho: = 7.00

Ha: 7.00

B)

The test statistics,

t =( - )/ (s /n)

= ( 6.89 - 7 ) / ( 2.11 / 185 )

= -0.709

C)

P-value = 0.2396

The p-value is p = 0.2396 > 0.05, it is concluded that the null hypothesis is not rejected.

There is not enough evidence to test the claim that the population mean of such ratings is less than 7.00. at 0.05 significance level.