Question

A data set about speed dating includes like ratings of male dates made by the female dates. The summary statistics are n=183, x=7.58 s=1.87. Use a 0.10 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 bull and alternative hypothesis, test statistic, P-value and state the final conclusion that address the original claim

Answer 1

The hypotheses are:

Null hypothesis

Alternate hypothesis

Since Sample standard deviation is given hence t left tailed test is used here

Rejection region:

Reject Ho if T_obs<t_0.10,182=1.28155

Test statistics:

Test statistics is calculated as

Hence T=-3.03832

P value :

P value computed from t statistics chart or by calculator as

P value=0.001366

Conclusion:

Since T_obs<t_0.10,182=1.28155 and P value=0.001366<0.01, hence we reject the null hypothesis and conclude that at 0.10 level of significance we have enough evidence to support the claim.