Question

6. Tudor brand car batteries are sold with the claim that they will last for at least 4 years. Weibang, having boosted his car (with a 3.5-year-old Tudor battery) many times this past winter, believes that the mean battery life is less than four years. A random sample of eight batteries was taken. The batteries were operational for the following time periods (months): 40, 41, 52, 48, 44, 47, 45, 43. (s =3.9 months). At the 5% significance level, can Weibang support his claim that Tudor batteries last less than four years?

Answer 1

Sample size = n = 8

The batteries were operational for the following time periods (months): 40, 41, 52, 48, 44, 47, 45, 43.

The batteries were operational for the following time periods (years): Divides by 12 to each value.

3.3333

3.4167

4.3333

4.0000

3.6667

3.9167

3.7500

3.5833

Sample mean = = 3.75

Standard deviation = s = 0.3273

Claim:  The mean battery life is less than four years.

The null and alternative hypothesis is

Level of significance = 0.05

Here population standard deviation is unknown so we have to use the t-test statistic.
Test statistic is

Degrees of freedom = n - 1 = 8 - 1 = 7

Critical value = 1.895    ( Using t table)

Test statistic | t | > critical vaue we reject null hypothesis.

Conclusion: Yes, we can Weibang support his claim that Tudor batteries last less than four years.