# Statistics , GSMN 261/261-T Fall 2017 Homework #6

Touro College

Statistics , GSMN 261/261-T                        Fall 2017

Homework  #6

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1. Use the significance level α, and confidence interval for estimating the population mean μ. Assume that population has a normal distribution.

An insurance company needs information about repairing costs of car being in accidents. A random sample of 25 cars has been drawn with a mean x = \$1500 and standard deviation s = \$300. Find 95% confidence interval for a true mean of all cars being in accidents.

1. Find 95%  confidence interval  for  estimating population standard deviation  σ  of car

batteries given that a random sample of 20 batteries has a standard deviation s = 1.25  years.

1. Test the claim that a population mean exceeds 40. You have a sample of 50 items for which the sample mean x = 42 and sample standard deviation s = 8. Use significance level α = 0.05.
2. In the study of the wide ranges in the academic success of college freshmen, one obvious factor is the amount of time spent studying. At the 0.05 significance level, test the claim that the standard deviation is more than 4.50 hours. The sample consists of 20 randomly selected freshmen who have a standard deviation of 5.75 hours.
3. Suppose that you want to decide which of two equally-priced brands of light bulbs lasts longer. You choose a random sample of 100 bulbs of each brand and find that brand A has a sample mean 1150 hours and a sample standard deviation of 70 hours, and that brand B has sample mean of 1170 hours and sample standard deviation of 80 hours. What decision should you make at 2%  significance level?

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