Question

A data set about speed dating includes "like" ratings of male dates made by the female dates. The summary statistics are n= 195, x= 5.88, s= 2.06. Use a 0.05 significance level to test the claim that the population mean of such ratings is less than 6.00. 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.

Answer 1

Here,

Sample mean \(=\bar{x}=5.88\)

Sample \(S . D=s=2.06\)

Sample size \(=n=195\)

Degrees of freedom \(=194\)

Significance Level \(=\alpha=0.05\)

Step 1: \(H_{0}: \mu=6\)

\(H_{1}: \mu<6\) (Left tailed test)

Step 2: The test statistic is, \(t=\frac{\bar{x}-\mu}{\left(\frac{s}{\sqrt{n}}\right)}=-0.81\)

Step \(3: P-\) value \(=P(t<-0.81)=0.209\)

Step \(4:\) We fail to reject \(H_{0} .\) There is not sufficient evidence to conclude that the mean of the population of ratings is less than \(6.00\).