Question

40 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 40 values have a mean of 51 sec and a standard deviation of 188 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=188 sec.) (a) The test statistic is (b) The P - value is

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :   = 0

H_a :    0

Test statistic = z

= ( - ) / / n

= (51 - 0) / 188 / 40

= 1.72

P(z > 1.72) = 1 - P(z < 1.72) = 0.0427

P-value = 2 * 0.0427 = 0.0854