Question

a data set about speed dating includes \like\ ratings of male dates made by the female dates. the summary statistics are ( n = 184 ), ( overline{x}=5.55 ), ( s = 1.87 ). use a 0.01 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.
what are the null and alternative hypotheses?
○ a. ( h_0:mu = 6.00 )
( h_1:mu>6.00 )
○ b. ( h_0:mu = 6.00 )
( h_1:mu
eq6.00 )
○ c. ( h_0:mu = 6.00 )
( h_1:mu<6.00 )
○ d. ( h_0:mu<6.00 )
( h_1:mu>6.00 )

Explanation:

Step1: Determine the null and alternative hypotheses

The null hypothesis \(H_0\) is a statement of equality. The claim is that the population mean \(\mu\) is less than \(6.00\). So, the null hypothesis \(H_0:\mu = 6.00\) (the status - quo or default assumption), and the alternative hypothesis \(H_1:\mu<6.00\) (the claim we are testing for).

Answer:

C. \(H_0:\mu = 6.00\), \(H_1:\mu<6.00\)