Question

45 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 45 values have a mean of 98sec and a standard deviation of 192sec. Use a 0.01 significance level to test the claim that the population of all watches has a mean of 0sec.

The test statistic is

The P-Value is

The final conclustion is

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

Answer 1

H0: = 0

Ha: 0

Test statistics

t = - / S / sqrt(n)

= 98 - 0 / 192 / sqrt(45)

= 3.42

This is test statistics value.

P-value = 2 * P( Z > z)  

= 2 * P (Z > 3.42)

= 2 * 0.0003

= 0.0006

Since p-value < 0.01 level, we have sufficient evidence to reject H0.

Conclusion -

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