Question

A local retailer claims that the mean lifetime of its lithium batteries is normally distributed with a mean of 1400 hours. A homeowner randomly selects 29 of these batteries and finds the mean lifetime to be 1380 hours with a standard deviation of 50 hours. Test the manufacturer’s claim. At an ? = .1, test the retailer’s claim. a.) State the null and alternative hypotheses. b.) Verify that the requirements are met for conducting the hypothesis test. c.) Conduct the test of hypothesis with the classical approach.

Answer 1

a)

n29 > x = 1380 ya=0.1 s Given - Mo = 1400 50 9) To test: Ho li = 1400 Vs. Hi u # 1400 b) c) t Test statistics - x - 시이 sin 1380 -1400 50 L 29 t =-2.154 at 2-0.) d. = 29-1=28 weget, -) tci 1.701 decision sule : if it to we reject Ho. Accept otherwise. Here It): 2.154 &tc=1.701 reject Ho so we

Conclusion - we do not have sufficient evidence to conclude the claim that the mean lifetime of its lithium batteries is normally distributed with a mean of 1400 hours.

b) The assumptions of the one-sample t-test are:
1. The data are continuous (not discrete).
2. The data follow the normal probability distribution.
3. The sample is a simple random sample from its population. Each individual in the population has an equal
probability of being selected in the sample.

All assumptions are fulfilled.

Hit like please.