Question

A factory that manufactures bolts is performing a quality control experiment. Each object should have a length of no more than 20 centimeters. The factory believes that the length of the bolts exceeds this value and measures the length of 64 bolts. The sample mean bolt length was 20.06 centimeters. The population standard deviation is known to be σ=0.16 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=0.1?

Answer 1

Step 1 :

Ho: 20

Ha:   20

Null hypothesis states that each object has a lengh of 20 cm or less.

Step 2: test stattistics

n = 64

sample mean = = 20.06

= 0.16

Assuming that the data is normally distributed. Also as the population SD is given, we will use z statistics

P value = P(z = 3)

P ( Z>3 )=1−P ( Z<3 )=1−0.9987=0.0013

Step 3 Conclusion:

The z-critical value for a right-tailed test, for a significance level of α=0.1. zc=1.28

As the z stat ( 3) falls in the rejection area, we reject the Null hypothesis.

Since the P value (0.0013) is less than level of significane (0.10), we reject the Null hypothesis.

Hence sufficient evidence exists that the length of bolts is actually greater than 20 at a significance level of α=0.1