Question

A manufacturer claims that the mean life time of its lithium batteries is 1500 hours . A home owner selects 30 of these batteries and finds the mean lifetime to be 1470 hours with a standard deviation of 80 hours. Test the manufacturer's claim. Use=0.05. Round the test statistic to the nearest thousandth.

a) Hypothesis:

b)Critical value (t critical):

c)Test statistic (tstat) and the decision about the test statistic:(reject or fail to reject Ho):

d)Conclusion that results from the decision about Ho,how would you politely address the manufacturer’s claim?

Answer 1

a) The null and alternative hypothesis is ,

The test is two-tailed test.

b) Since , the population standard deviation is not known.

Therefore , use t-distribution.

Now , df=degrees of freedom=n-1=30-1=29

The critical value is ,

; From t-table

c) The test statistic is ,

d) Decision : here , the value of the test statistic lies in the rejection region.

Therefore , reject the null hypothesis.

Conclusion : Hence , there is not sufficient evidence to support the manufacturer's claim that the mean life time of its lithium batteries is 1500 hours.