Question

(1 pt) 50 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 50 values have a mean of 75 sec and a standard deviation of 234 sec. Use a 0.02 significance level to test the claim that the population of all watches has a mean of 0 sec. (Assume σ=234 sec.)

(a) The test statistic is

(b) The P - value is

(c) The final conclusion is

A. The results are statistically significant. There is evidence that the mean is not equal to 0.
B. The results are not statistically significant. There is insufficient evidence to claim that the mean is not equal to 0.

Answer 1

H0: = 0

Ha: 0

a)

Test statistics

z = - / / sqrt(n)

= 75 - 0 / 234 / sqrt(50)  

= 2.27

b)

p-value = 2 * P( Z > z)

= 2 * P( Z > 2.27)

= 2 * 0.0116

= 0.0232

Since p-value > 0.02 level, we do not have sufficient evidence to reject H0.

c)

Conclusion -

The results are not statistically significant. There is insufficient evidence to claim that the

mean is not equal to 0