Question

. A data set about speed dating includes "like" ratings of male dates made by the female dates. The summary statistics are n. 185, 783,8 2 27. Use a 0.05 significance level to test the claim that the population mean of such ratings is less than 8.00. 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? OAH: -8.00 OB. H: 8.00 H78.00 H>8.00 OCH: 8.00 OD. M:*8.00 Her<8.00 Determine the best statistic Round to two decimal places as needed.) State the final conclusion that addresses the original claim. Hy. There is evidence to conclude that the mean of the population of ratings is swers Fall to roject Roject

Answer 1

Solution:

Here, we have to use one sample t test for the population mean.

The null and alternative hypotheses are given as below:

H₀: µ = 8.00

H₁: µ < 8.00

(Answer: D)

This is a lower tailed test.

The test statistic formula is given as below:

t = (Xbar - µ)/[S/sqrt(n)]

From given data, we have

µ = 8

Xbar = 7.83

S = 2.27

n = 185

t = (Xbar - µ)/[S/sqrt(n)]

t = (7.83 - 8)/[2.27/sqrt(185)]

t = -1.0186

Test statistic = -1.02.

df = n – 1 = 184

α = 0.05

Critical value = -1.6532

(by using t-table or excel)

P-value = 0.1549

(by using t-table)

P-value > α = 0.05

So, we do not reject the null hypothesis

Fail to reject H₀. There is not sufficient evidence to conclude that the mean of the population ratings is less than 8.00.