Question

a data set about speed dating includes \like\ ratings of male dates made by the female dates. the summary statistics are ( n = 186 ), ( \bar{x}=6.80 ), ( s = 2.22 ). use a 0.05 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, lest statistic, p-value, and state the final conclusion that addresses the original claim.
what are the null and alternative hypotheses?
a ( h_{0}: mu = 7.00 )
( h_{1}: mu < 7.00 )
b ( h_{0}: mu = 7.00 )
( h_{1}: mu > 7.00 )
c ( h_{0}: mu = 7.00 )
( h_{1}: mu
eq 7.00 )
d ( h_{0}: mu < 7.00 )
( h_{1}: mu > 7.00 )
determine the test statistic.

• 0.67 (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 \(n = 186\), so \(df=186-1 = 185\)

Step2: Find the P - value using the test - statistic

We have a one - tailed \(t\) - test (left - tailed since \(H_1:\mu<7.00\)) with \(t=- 0.67\) and \(df = 185\).
Using a \(t\) - distribution table or technology (such as a TI - 84 Plus: tcdf(-1000,-0.67,185)), the P - value is calculated.
The P - value for \(t=-0.67\) and \(df = 185\) is approximately \(0.252\)

Answer:

The P - value is \(0.252\)