Question

ACME Manufacturing claims that its cell phone batteries last more than 32 hours on average in a certain type of cell phone. Tests on a random sample of 18 batteries showed a mean battery life of 37.8 hours with a population standard deviation of 10 hours. Is the mean battery life greater than the 32 hour claim? Answer the following questions using a significance level of alpha = 0.05.

Answer 1

Answer:

We can conclude that the battery life is greater than the 32 hour claim.

Step-by-step explanation:

The null hypothesis is:

$H_{0} = 32$

The alternate hypotesis is:

$H_{1} > 32$

Our test statistic is:

$t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}$

In which X is the statistic, $\mu$ is the mean, $\sigma$ is the standard deviation and n is the size of the sample.

In this problem, we have that:

$X = 37.8, \mu = 32, \sigma = 10, n = 18$

So

$t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

$t = \frac{37.8 - 32}{\frac{10}{\sqrt{18}}}$

$t = 2.46$

We need to find the probability of finding a mean time greater than 37.8. If it is 5% of smaller(alpha = 0.05.), we can conclude that the battery life is greater than the 32 hour claim.

Probability of finding a mean time greater than 37.8

1 subtracted by the pvalue of z = t = 2.46.

z = 2.46 has a pvalue of 0.9931

1 - 0.9931 = 0.0069 < 0.05

So we can conclude that the battery life is greater than the 32 hour claim.