# Notes on One-Sample Mean Tests

```Hypothesis Tests for
Population Means
Section 10-4
Warm-Up
http://goo.gl/forms/ICVv9pe7Bd
Remember: Sampling Distribution of
Means
 x  
   
x
n
Approximately Normal
If population is normal
If n30 (CLT)
Use the z Test Statistic if  is known
and it’s a large sample
z
x

n
Assumptions:
1. SRS
2. Approx Normal – since n&gt; 30 or pop is
normal
3. Independent (10 * n)
If population standard deviation is
unknown or n&lt;30: Use T-Distribution
Use tcdf (beginning, end, df)
Assumptions
SRS
Approximately Normal
n&lt; 30: Use t unless there are outliers or the
data is really skewed.
n30: 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?
```