Hypothesis Tests for Population Means

Section 10-4

Warm-Up

http://goo.gl/forms/ICVv9pe7Bd

Remember: Sampling Distribution of Means

Approximately NormalIf population is normalIf n30 (CLT)

x

x n

Use the z Test Statistic if is knownand it’s a large sample

xz

n

Assumptions: 1. SRS

2. Approx Normal – since n> 30 or pop is normal

3. Independent (10 * n)

If population standard deviation is unknown or n<30: Use T-Distribution

Use tcdf (beginning, end, df)

Assumptions

SRSApproximately Normal

n< 30: Use t unless there are outliers or the data is really skewed.

n30: Use t (if is unknown), data can be skewed

Use boxplots to check for skewness

Independent

A researcher reports that the average salary of assistant professors is more than $42,000. A sample of 30 assistant professors has a mean salary of $43,260. At = 0.05, test the claim that assistant professors earn more than $42,000 a year. The standard deviation is $5,230.

A national magazine claims the average student watches less tv than the general public. The national average is 29.4 hours with a standard deviation of 2 hours. In a sample of 30, the mean is 27 hours. Using a confidence level of 0.01, is there enough evidence to support their claim?

The average salary for nurses is $24,000. A sample of 10 nurses has a mean of $23,450 and a standard deviation of $400. Is this really the mean salary. Use = 0.05.

A machine is designed to fill jars with 16 ounces of coffee. A consumer suspects that the machine is not filling the jars completely. They sampled 12 jars shown below. Is there enough evidence to support the consumer’s claim at = 0.10?

15 15.4 16.2 16.1 15.8 16.2

15.7 15.6 16 16.3 15.3 15.9

The Medical Rehabilitation Foundation reports that the average cost of rehabilitation for stroke victims is $24,672. to see if the average cost of rehabilitation is different at a large hospital, a researcher selected a random sample of 35 stroke victims and found that the average cost of their rehabilitation if $25,266. The st. dev. Is $3,251. At = 0.01, can it be concluded that the average cost at a large hospital is different?

A researcher wishes to test the claim that the average age of lifeguards is Ocean City is greater than 24 years. She selects a sample of 36 guards and finds the mean of the sample to be 24.7, with a st. dev. Of 2 years. Is there evidence to support the claim at = 0.05?

A physician claims that jogger’s maximal volume oxygen uptake is greater than the average of all adults. A sample of 15 joggers has a mean of 43.6 ml per kg and a standard deviation of 6 ml/kg. If the average of all adults is 36.7 ml/kg, is there enough evidence to support the physician’s claim at = 0.01?