Question

6. The Speedy oil change company advertised the mean completion time for an oil change is less than 15 minutes. A sample of 16 oil changes resulted in a mean of 14 minutes and standard deviation of 4 minutes. (a) At α=10%, using the classical approach to test the claim. (b) Using P-value approach to conclude it.

Answer 1

Given

n = 16

X_bar = 14

s = 4

1) Hypothesis:

H0 : = 15

H1: < 15

2) test statistic value is

Z = (x_bar - ​​​​​​) / (s/sqrt(n))

= (14-15)/(4/sqrt(16))

Z = -1.00

3) p value for Z test statistic is 0.1587

P value = 0.1587

4) conclusion:

P value (0.1587) is greater than 0.1 level of significance hence fail to reject null hypothesis. Therefore there is not sufficient evidence to conclude that the mean completion time for an oil change is less than 15 minutes.

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