Question

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

n=186​,

x=7.85​,

s=1.97.

Use a 0.05 significance level to test the claim that the population mean of such ratings is less than 8.00.

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?

Determine the test statistic

(Fail to reject or Reject) H0. There is (sufficient or insufficient) evidence to conclude that the mean of the population of ratings is (greater than or equal to or less than or not) 8.00

Answer 1

Here we want to test for the population mean. Since n > 30, we assume that the data is normal. Also the pop SD is not given so we will use the t-test for one population mean.

We wat to test if the mean ratings is less than 8. This is one left tailed test.

What are the null and alternative​ hypotheses?

=> 8

< 8

n =186   = 7.85 S_x  =1.97

Test Stat =

Where the null mean = 8

Test stat = -1.0384

p - value = P( > |Test Stat |)

=P(t₁₈₅ > 1.04) ...........using t-dist tables

p-value = 0.1498

Since p-value > 0.05 significance level

Fail to reject H0.

There is insufficient evidence to conclude that the mean of the population of ratings is less than  8.00