Question

A manufacturer claims that the mean lifetime of its lithium batteries is 1200 hours. A homeowner selects 25 of these batteries and finds the mean lifetime to be 1180 hours with a standard deviation of 80 hours. Test the manufacturer's claim. Use ΅ = 0.05. Round the test statistic to the nearest thousandth.

Answer 1

Since p is > α we fail to reject the Null as the result is not significant at α = 0.05

Explanation:

Given that:

Mean lifetime (m) = 1200

Sample size (n) = 25

Sample mean (x) = 1180

Standard deviation (s) = 80

α = 0.05

The null hypothesis :

H0 : m = 1200

Alternative hypothesis : m ≠1200

The t statistic :

(x - m) / (s/√n)

(1180 - 1200) / (80 / √25)

-20 / (80/5)

= - 1.250

P value = 0.10565 ( p value calculator)

Reject Null hypothesis if p > α

At α = 0.05

Since p is > α we fail to reject the Null as the result is not significant at α = 0.05