Question

A factory that manufactures bolts is performing a quality control experiment. Each object should have a length of no more than 12 centimeters. The factory believes that the length of the bolts exceeds this value and measures the length of 76 bolts. The sample mean bolt length was 12.06 centimeters. The population standard deviation is known to be 0.27 centimeters.

What is the test statistic z?

What is the p-value?

Does sufficient evidence exist that the length of bolts is actually greater than the mean value at a significance level of α=0.05?

Answer 1

Solution :

= 12

=12.06

=0.27

n = 76

This is the right tailed test .

The null and alternative hypothesis is ,

H0 :    = 12

Ha : > 12

Test statistic = z

= ( - ) / / n

= (12.06 -12) / 0.27 / 76

= 0.02

Test statistic = z = 0.02

P(z >0.02 ) = 1 - P(z < 0.02 ) = 1 - 0.5080

P-value =0.4920

= 0.05  

P-value <

0.4920 > 0.05

Fail to reject the null hypothesis .

There is insufficient evidence to suggest that