1. 9.3: Tests about a Population Mean
Chapter 9: Testing a Claim

2. Biologists studying the healing of skin wounds measured the rate at which new cells closed a cut made in the skin of an anesthetized newt. Here are data from a random sample of 18 newts, measured in micrometers per hour:
We want to estimate the mean healing rate, 𝜇.
Why a confidence interval and not a test???
Recall…

3. test statistic= stat−param stan. dev. of stat.
Since, from your formula sheet,
test statistic= stat−param stan. dev. of stat.
we can say that for a 𝑡-statistic:
𝑡= 𝑥 −𝜇 𝑠 𝑛
𝑡-statistic

4. Some comments on Table B. Take a look!
It only gives ranges for P-values.
It does not give values for all sample sizes (there are limited degrees of freedom listed). If what you need is not given, use the next smallest df.
It only gives positive 𝑡-scores – use symmetry to find a P-value for a negative 𝑡-score.
Some comments on Table B. Take a look!

5. State: Define the parameter (𝜇) and state the hypotheses.
Plan: State the name of the test and check conditions (random, normal, independent)
Do: Find the 𝑡-statistic and find the P-value; draw the curve!
Conclude: Conclude in context (include P-value, significance level, reject or fail to reject, and conclusion in context)
The 4-Step Process

6. Example: Doing a 𝑡-test by hand Less Music?
A classic rock radio station claims to play an average of 50 minutes of music every hour. However, it seems that every time you turn to this station, there is as commercial playing. To investigate their claim, you randomly select 12 different hours during the next week and record what the radio station plays in each of the 12 hours. Here are the number of minutes in each of these hours: Is this convincing evidence that the radio station plays less music then they claim?
Example: Doing a 𝑡-test by hand Less Music?

7. Example: Doing a 𝑡-test by hand Construction Zones
Every road has one at some point – construction zones that have much lower speed limits. To see if drivers obey these lower speed limits, a police officer used a radar gun to measure the speed (in mph) of a random sample of 10 drivers in a 25 mph construction zone. Here are the results: Can we conclude that the average speed of drivers in this construction zone is greater than the posted 25 mph speed limit?
Example: Doing a 𝑡-test by hand Construction Zones

8. Example: Doing a 𝑡-test by hand Construction Zones
Given your conclusion to the test, which kind of mistake – a Type I or a Type II error – could you have made? Explain what this mistake means in context.
Example: Doing a 𝑡-test by hand Construction Zones

9. Example: Pineapple 
At the Hawaii Pineapple Company, managers are interested in the sizes of the pineapples grown in the company’s fields. Last year, the mean weight of the pineapples harvested from one large field was 31 ounces. A new irrigation system was installed in this field after the growing season. Managers wonder whether this change will affect the mean weight of future pineapples grown in the field. To find out, they select an weigh a random sample of 50 pineapples from this year’s crop.
Do these data suggest that the mean weight of pineapples produced in the field has changed this year? Give appropriate statistical evidence to support your answer.
Example: Pineapple 

10. Example: Pineapple, Part 2 
Suppose that we were given the following computer output for the pineapple problem. How does it support our previous conclusion?
Example: Pineapple, Part 2 

11. Pg. 564: #57 – 60
Pg. 588: #71, 73, 83, 85
Homework