Question

energizer claims in their commercials that their batteries last on average exactly 500 hours. We want to collect enough data to disprove this. In a sample of 300 batteries, we see that these batteries last an average of 506 hours with a standard deviation of 70 hours.

(a) Determine the null and alternative hypotheses.

(b) Find the test statistic

(c) Should H0 be rejected

(d) based on your answer in part (c), what is your conclusion as it applies to THIS SITUATION. be specific.

Answer 1

a) H₀: = 500

    H₁: 500

b) The test statistic t = ()/(s/)

                                 = (506 - 500)/(70/)

                                 = 1.485

c) At 5% significance level the critical values are t^* = +/- 1.968

As the test statistic value is not greater than the upper critical value (1.485 < 1.968), we should not reject H₀.

d) So there is sufficient evidence to suport the claim that the bartteries last on average exactly 500 hours.