Answer to Question #221744 in Statistics and Probability for jairah

Question

2. A mobile company is innovating a new mobile phone and is interested how long it will take for a battery

to charge fully. The standard deviation is known to be 15 minutes. The company wishes to test if the

mean charging time is at most 30 minutes compared to the claim that it is more than 30 minutes. A

random sample of 35 mobile phones was selected and the mean charging time is more than 35

minutes. Can it be concluded that the mean charging time is not at most 30 minutes if the critical region

is greater than 35 minutes?

Answer 1

$\sigma = 15 \\ n=35 \\ \bar{x} > 35 \\ H_0: \mu>30 \\ H_1: \mu<30$

One-tail test.

Test-statistic:

$Z= \frac{\bar{x} - \mu}{\sigma / \sqrt{n}} \\ Z = \frac{35-30}{15 / \sqrt{35}} = \frac{5}{2.535} = 1.972$

Let use α=0.05

Reject H₀ if $Z< -Z_{crit}$

$Z_{crit}= -1.96 \\ Z=1.972 > Z_{crit}$

Accept H₀. Can it be concluded that the mean charging time is NOT at most 30 minutes at 0.05 significance level.