Question

4040 people are randomly selected and the accuracy of their wristwatches is checked, with positive errors representing watches that are ahead of the correct time and negative errors representing watches that are behind the correct time. The 4040 values have a mean of 9191sec and a standard deviation of 174174sec. Use a 0.020.02 significance level to test the claim that the population of all watches has a mean of 00sec.

The test statistic is

The P-Value is

The final conclustion is

A. There is not sufficient evidence to warrant rejection of the claim that the mean is equal to 0
B. There is sufficient evidence to warrant rejection of the claim that the mean is equal to 0

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :   = 0

H_a : 0

= 91

= 0

= 174

n =40

Test statistic = z

= ( - ) / / n = (91 - 0) / 174 / 40

Test statistic = 0.0827

This is the twotailed test .

P(z > 0.0827) = 1 - P(z < 0.0827) = 1 - 0.533 = 0.4670

P-value = 0.4670

= 0.02

P-value >

Fail to reject the null hypothesis .

B. There is sufficient evidence to warrant rejection of the claim that the mean is equal to 0 .