Review – Exam 3Sampling Distributions

Confidence IntervalsHypothesis Testing

Sampling Distributions

n=9n=36

Practice 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?

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.

Confidence Interval

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%?

Using the t-table

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?

Sample Size

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?

Formulate the Hypothesis

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?

Testing Error

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?

Hypothesis Testing

Height

Weight

77 235

70 170

63 125

62 110

72 185

71 298

69 200

72 266

69 270

68 175

p-valueMy null hypothesis is that the population mean height = 66 inchesOne-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 0.041Consider a significance level of .05.

Based on this sample data, should I accept or reject my null hypothesis? Why?