**Touro**** College**

**Statistics ,** **GSMN 261/261-T ** **Fall 2017**

**Homework #6 **

**Instructor: **

**Student Name: ——————————-**

- Use the significance level
**α**, and confidence interval for__estimating the population____mean__. Assume that population has a normal distribution.**μ**

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.

- 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.

- Test the claim that a
__population mean exceeds__. You have a sample of**40****50**items for which the sample mean**x = 42**and sample standard deviation**s = 8**. Use significance level**α = 0.05**. - 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__. The sample consists of**4.50**hours**20**randomly selected freshmen who have a standard deviation of**5.75**hours. - 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__hours and a**1150**__sample standard deviation of__hours, and that**70**__brand B__has__sample mean of__hours and**1170**__sample standard deviation of__hours. What decision should you make**80**__at__**2%**significance level?