Question

True or False: The life in hours of a battery is known to be approximately normally distributed, with standard deviation of 15 hours. A random sample of 16 batteries has a mean life of 110 hours. Based on sampling results, there is sufficient evidence on this sample to support the claim that battery life exceeds 100 hours at α=0.05.

Answer 1

Solution:

It is TRUE

Given ,

claim : > 100

n = 16

= 110

= 15

Use = 0.05

Hypothesis are

H0 : = 100

H1 :   > 110

b)The test statistic z is given by

z =

= (100 - 100) / (15/16)

= 2.67

Now , observe that ,there is > sign in H1. So , the test is right tailed.

p value = P(Z > 2.67)

= P(Z < -2.67)

= 0.0038 (use z table)

Since the p value is less than = 0.05 , we reject the null hypothesis.

There is sufficient evidence on this sample to support the claim that battery life exceeds 100 hours at α=0.05.

So , TRUE