a) A battery manufacturer claims that battery life is 80 hours. Since we know that not all batteries will last exactly 80 hours, we understand that the claim really is that the mean life is 80 hours. Do we have reason to doubt this claim after we test 25 batteries and find that the mean life for the sample was 70 hours with a standard deviation of 20 hours?

i) State the null hypothesis as a precise formula.

ii) Why would we use a one-tailed t-test, with an alpha of .05 for this problem?

Explain in your own words why these are good choices.

iii) What are the degrees of freedom?

iv) Carry out the calculation of t (the test statistic), explaining each part of the formula.

v) What is the critical value to which we compare the computed value of t? Explain what the critical value means.

vi) Did the absolute value of the computed t exceed the critical value?

vii) What is your conclusion about the batteries. Explain it in plain English.

b) Redo this problem with the following values; change the values one at a time, keeping the other information the same.

i) Sample means: 79, 60, and 75.

ii) Sample standard deviations: 5, 15, and 30.

iii) Sample size: 49, 100, and 1,600. (Remember to change the degrees of freedom accordingly!)

iv) Alpha set at .01.