Question

A cell phone manufacturer claims that, if properly charged, their phone batteries will operate for 48 hours. A study of 5000 batteries is undertaken and 15 stop operating in under 48 hours. Do these results support a claim that less than 0.2 percent of the company’s batteries will fail during the 48 hour period? Use a hypothesis test with ?=0.01. Be sure to explicitly state: The null and alternative hypotheses The test statistic equation and value Your conclusion

Answer 1

Here we have follwoing information:

Hypotheses are:

Standard deviation of the proportion is:

Test statistics will be:

Alternative hypothesis shows that the test is left tailed so p-value of the test is

p-value = P(z < 1.67) = 0.9525

Since p-value of the test is greater than 0.01 so we fail to reject the null hypothesis at 0.01 level of significance. So based on this sample, there is no support for the claim that less than 0.2 percent of the company’s batteries will fail during the 48 hour period.

Excel function used for p-value : "=NORMSDIST(1.67)"