Question

A company claims their new cell phone model has a mean battery life of 60 hours. A consumer group suspects this claim is exaggerated so they record the battery life of 100 randomly selected cell phones of this model and conduct a hypothesis test. The sample gives a mean life of 58 hours and a standard deviation of 10. Use this information to answer the following questions.

a. What is the null hypothesis about the population mean battery life?

b. What is the alternative hypothesis about the population mean battery life?

c. What is the standard score (z statistic) for the sample mean?

d. What is the P-value?

e. Would you reject the null hypothesis at the 5% significance level?

f. Would you reject the null hypothesis at the 1% significance level?

Answer 1

a. What is the null hypothesis about the population mean battery life?

null hypothesis:

The mean battery life is equal to 60

Ho: μ = 60

b. What is the alternative hypothesis about the population mean battery life?

alternate hypothesis:

The mean battery life is less than 60

Ha: μ < 60

This corresponds to a left-tailed test, for which a t-test for one mean, with unknown population standard deviation will be used.

c. What is the standard score (z statistic) for the sample mean?

The t-statistic is computed as follows:

d. What is the P-value?

The p-value is p = 0.0228

e. Would you reject the null hypothesis at the 5% significance level?

since p = 0.0241 < 0.05, it is concluded that the null hypothesis is rejected.

f. Would you reject the null hypothesis at the 1% significance level?

since p = 0.0241 ≥0.01, it is concluded that the null hypothesis is not rejected.