Question

A data set about speed dating includes​ "like" ratings of male dates made by the female dates. The summary statistics are n=194​, x overbar=6.81​, s=1.91. 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 and H1​: μ>7.00

B. H0​: μ=7.00 and H1​: μ>7.00

C. H0​: μ=7.00 and H1​: μ<7.00

D. H0​: μ=7.00 and H1​: μ≠7.00

Determine the test statistic. ___ (round two)

State the final conclusion that addresses the original claim.

Reject or Fail to reject ____

There is ___ (not sufficient, sufficient) evidence to conclude that the mean of the population of ratings is ___ (not, less than, equal to, greater than) 7.00.

Answer 1

Solution :

= 7.00

=6.81

S =1.91

n = 194

This is the left tailed test .

The null and alternative hypothesis is ,

H0 :    = 7.00

Ha : < 7.00

Test statistic = t

= ( - ) / S / n

= (6.81 -7.00 ) /1.91 / 194

= -0.046

Test statistic = t =  -0.05

P-value =0.4817

= 0.05  

P-value >

0.4817 > 0.05

Fail to reject the null hypothesis .

There is not sufficient, evidence to conclude that the mean of the population of ratings is to, greater than 7.00