1. Sampling Distributions Confidence Intervals Hypothesis Testing

2. n=9 n=36

3.  The average weight of a cell phone is 5.7 ounces. Assuming a population σ of 2.0 ounces and a random sample of 49 phones, what is the probability the average weight for the sample will be ≥ 6.2 ounces?  If the sample size had been 12 instead of 49, what further assumption must we make in order to solve this problem?

4.  A random sample of 30 students has been selected from those attending ESCC. The average number of hours they spent in the school library last week was 5.21 with a sample standard deviation of 1.18 hours.  Construct a 90% confidence interval for the population mean.

5.  For a sample size of n = 22, what t values would correspond to an area centered at t = 0 and having an area beneath the curve of 90%?  For a sample size of n = 200, what t values would correspond to an area centered at t = 0 and having an area beneath the curve of 95%?

6.  A package-filling machine has been found to have a standard deviation of 0.65 ounces. A random sample will be conducted to determine the average weight of product being packed by the machine.  To be 95% confident that the sample mean will not differ from the actual population mean by more than 0.1 ounces, what sample size is required?

7.  I predict the mean score for the next exam will be 92% or higher. The mean turns out to be 90%. Was I wrong?  The owner of the Montgomery Biscuits claims average attendance at home games is 3,456. A survey of the 12 home games in July showed average attendance to be 3,012. Was the owner’s claim accurate?  My employee stated that less than 25% of the people working in Daleville are in a retirement plan. A survey of 20 employees shows only 4 are in a plan. Was the boss correct?

8.  I predict the population mean score for an exam will be 92%. After taking a sample of 8 and finding the mean score from the sample to be 99.4%, I conduct a t-test at a.90 significance level and reject the null hypothesis.  After teaching the same class for many years and giving the same exam, I discover that the mean for all students is very close to 92%.  What type of error did I make with the results of the first t-test? Why?

9.  Joe’s Tire Company claims their tires will last at least 60,000 miles in highway driving conditions.  The editors of Tire magazine doubt this claim, so they select 31 tires at random and test them. The tires they tested had a mean life of 58,341.69 miles and a standard deviation of 3,632.53 miles.  Is Joe’s claim accurate?

10. HeightWeight 77235 70170 63125 62110 72185 71298 69200 72266 69270 68175 My null hypothesis is that the population mean height = 66 inches One-Sample T: Height Test of mu = 66 vs not = 66 Variable N Mean StDev SE Mean 95% CI Height 10 69.30 4.37 1.38 (66.17, 72.43) T P 2.39 0.041 Consider a significance level of.05. Based on this sample data, should I accept or reject my null hypothesis? Why?