Question

A cell phone's battery life is important when making a purchase. The Samsung Galaxy is said to have a mean battery life of 8 hours. In a random sample of size 14, the mean battery life was 8.22 hours. Population standard deviation is known to be 1 hour. Conduct a test where Ho: mu = 8 against Ha: mu ≠ 8.

a) Calculate the appropriate test statistic.

b) Determine the p-value and include a labeled picture.

c) At significance of 0.05, state your conclusion in terms of the problem.

Answer 1

$\\ H_0:\mu=8\\\\ H_1:\mu \neq8\\\\ a.)Test~Statistic(Z)=\frac{\bar{x}-\mu}{\sigma/\sqrt{n}}=\frac{8.22-8}{1/\sqrt{14}}=0.82\\\\ b.)p-value=p(|Z|>0.82)\\\\ ~~~~~~~~~=0.4122\\\\$

c.)

P-value is less than significance(alpha=0.05), fail to reject Null Hypothesis.

There is not enough to support the claim that true mean is different than 8.