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.

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

Step-by-step explanation:

The null hypothesis is:

The alternate hypotesis is:

Our test statistic is:

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

In this problem, we have that:

So

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.

180

step-by-step explanation:

12-2=10

20-2=18

18x10=180