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Galina-37
2 months ago
14

A house cleaning service claims that it can clean a four bedroom house in less than 2 hours. A sample of n = 16 houses is taken

and the sample mean is found to be 1.97 hours and the sample standard deviation is found to be 0.1 hours. Using a 0.05 level of significance the correct conclusion is:(A) reject the null because the test statistic (-1.2) is < the critical value (1.7531).(B) do not reject the null because the test statistic (-1.2) is > the critical value (-1.7531).(C) reject the null because the test statistic (-1.7531) is < the critical value (-1.2).(D) do not reject the null because the test statistic (1.2) is > the critical value (-1.7531).
Mathematics
1 answer:
Zina [12.3K]2 months ago
3 0

Response:

Option B is correct

Step-by-step breakdown:

H_0: x bar =2\\H_a: x bar

(One-tailed test at a significance level of 5%)

n = 16 and x̄ = 1.97

s = 0.1

Standard error of the mean = \frac{s}{\sqrt{n} } \\=0.025

Difference in means = 1.97-2 =-0.03

t statistic = Difference in means/se = -1.2

degrees of freedom = 16 - 1 = 15

p-value = 0.124375

(B) do not reject the null hypothesis since the test statistic (-1.2) is > the critical value (-1.7531).

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