Question

a data set about speed dating includes \like\ ratings of male dates made by the female dates. the summary statistics are ( n = 191 ), ( overline{x}=6.51 ), ( s = 1.96 ). use a 0.10 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.

a. ( h_0:mu = 7.00 )
( h_1:mu
eq7.00 )
b. ( h_0:mu = 7.00 )
( h_1:mult7.00 )
c. ( h_0:mu = 7.00 )
( h_1:mugt7.00 )
d. ( h_0:mult7.00 )
( h_1:mugt7.00 )
determine the test statistic.
-3.45 (round to two decimal places as needed.)
determine the p - value.
(round to three decimal places as needed.)

Explanation:

Step1: Determine the degrees of freedom

The degrees of freedom \(df=n - 1\). Given \(n = 191\), so \(df=191-1 = 190\)

Step2: Find the P - value

Since the test statistic \(t=-3.45\) and it is a left - tailed test (\(H_1:\mu<7.00\)).
Using a t - distribution table or a calculator with a t - distribution function (such as in Excel: \(=T.DIST(-3.45,190,TRUE)\)), we find the P - value.
The P - value is the probability that \(T

Answer:

The P - value is approximately \(0.000\) (rounded to three decimal places).