Question

a data set about speed dating includes \like\ ratings of male dates made by the female dates. the summary statist are ( n = 184 ), ( overline{x}=6.83 ), ( s = 2.07 ). use a 0.10 significance level to test the claim that the population mean of such rating 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.
what are the null and alternative hypotheses?
a. ( h_0:mu = 7.00 )( h_1:mult7.00 )
b. ( h_0:mu = 7.00 )( h_1:mugt7.00 )
c. ( h_0:mu = 7.00 )( h_1:mu
eq7.00 )
d. ( h_0:mult7.00 )( h_1:mugt7.00 )
determine the test statistic.

• 1.11 (round to two decimal places as needed.)

determine the p - value.
(round to three decimal places as needed.)

Explanation:

Step1: Determine the P - value

Since this is a left - tailed test (because \(H_1:\mu<7.00\)) and the test statistic \(t=- 1.11\) with \(n = 184\), the degrees of freedom \(df=n - 1=184 - 1 = 183\).
Using a t - distribution table or a calculator (for a t - distribution, the P - value for a left - tailed test with test statistic \(t\) and \(df\) is \(P(T<t)\)).
Using a calculator or software (e.g., in Excel, if using the function T.DIST(-1.11,183,TRUE)), we calculate the P - value.

Step2: Calculate the P - value

\(P(T < - 1.11)\) with \(df = 183\).
Using a standard normal approximation (since for large \(n\) (here \(n=184\)) the t - distribution is close to the standard normal distribution), or a more accurate t - distribution calculation.
The P - value is approximately \(0.134\)

Answer:

\(0.134\)