Question

Standby time is amount of time a phone can remain powered on while not being used. A cell phone company claims that the standby time of certain phone model is 16 days on average. A consumer report firm gathered a sample of 19 batteries and conducted tests on this claim. The sample mean was 15 days and 10 hours and the sample standard deviation was 30 hours. Assume that the standby time is distributed as normal. In testing if the average standby time is shorter than 16 days, compute the value of the test statistic (round off to second decimal place).

Answer 1

Answer:

$t_{stat} = -2.03$

Step-by-step explanation:

We are given the following in the question:  

Population mean, μ = 16 days = 384 hours

Sample mean, $\bar{x}$ = 15 days 10 hours = 370 hours

Sample size, n = 19

Sample standard deviation, s = 30 hours

First, we design the null and the alternate hypothesis

$H_{0}: \mu = 384\text{ hours}\\H_A: \mu < 384\text{ hours}$

We use one-tailed t test to perform this hypothesis.

Formula:

$t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }$

Putting all the values, we have

$t_{stat} = \displaystyle\frac{370 - 384}{\frac{30}{\sqrt{19}} } = -2.03415 \approx -2.03$

The value of t-statistic is -2.03