A battery company claims that its batteries last an average of 100 hours under normal use. There have been several complaints that the batteries don’t last that long, so an independent testing agency is engaged to test them. For the 16 batteries the agency tested, the mean lifetime was 97 hours with a standard deviation of 12 hours.

a) What are the null and alternative hypotheses?

b) A consumer advocate (who does not know Statistics) says that 97 hours is a lot less than the advertised 100 hours, so we should reject the company’s claim. Explain to him the problem with doing that.

c) What assumptions must we make in order to proceed with inference?

d) At a 5% level of significance, what do you conclude?

e) Suppose that, in fact, the average life of the company’s batteries is only 98 hours. Has an error been made in (d)? If so, what kind?