Question

a data set about speed dating includes \like\ ratings of male dates made by the female dates. the summ 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 s 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 cl 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. (round to two decimal places as needed.)

Explanation:

Step1: Calculate the test statistic

The formula for the \(t\)-test statistic in a one - sample \(t\) - test is \(t=\frac{\bar{x}-\mu}{s/\sqrt{n}}\).
Here, \(\bar{x} = 6.83\), \(\mu = 7.00\), \(s = 2.07\), and \(n = 184\).
Substitute the values into the formula:

$$t=\frac{6.83 - 7.00}{2.07/\sqrt{184}}$$

First, calculate the denominator \(2.07/\sqrt{184}\approx2.07/13.5646\approx0.1526\)
Then, calculate the numerator \(6.83 - 7.00=- 0.17\)
So, \(t=\frac{-0.17}{0.1526}\approx - 1.11\)

Answer:

The test statistic is \(-1.11\)