MONDAY, FEB. 26TH SECTION 9.3 DAY 2

•  Today, you will perform a significance test about a population mean μ.

•  You will use a confidence interval to draw a conclusion for a two-sided test about a population parameter.

•  You will understand how to use tests wisely and increase power.

LEARNING OBJECTIVES

At the Hawaiian 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 different irrigation system was installed in this field after the growing season. Managers wonder how this change will affect the mean weight of pineapples grown in

the field. To find out, they select and weigh a random sample of 50 pineapples from this year’s crop. The Minitab output below summarizes the data:

       

Do these data provide convincing evidence that the mean weight of pineapples produced in the field has changed this year?

EXAMPLE 1

STATE

PLAN

DO

•  P-value:Tcdf(lower: -100000, upper: -2.762, df: 49) =P-value = 0.00403 x 2 = 0.008065Check: Using the calculator T-Test command with df = 50 – 1 = 49, we get t = 2.762 and a P-value of 0.00807.

CONCLUDE

Confidence Intervals Give More Information than Significance Tests

  Significance tests give us convincing evidence of

whether or not the true mean μ differs from the null hypothesis μO. Unfortunately, significance tests do not give us any idea of what the actual value of μ is. That is why we still need confidence intervals- they provide a set

of plausible values for the population mean μ.  

Minitab output for a significance test and confidence interval based on the pineapple data is shown below. The test statistic and P-value match what we

got earlier (with the exception of rounding):

 

 

 

 

Interpret the 95% confidence interval in context. Explain how the confidence interval leads to the same conclusion as the previous example.

EXAMPLE 1 CONTINUED:

We are 95% confident that the interval from 31.255 to 32.616 ounces captures the true mean weight of this year’s pineapple

crop.

This confidence interval does not include 31 as a plausible value, which aligns with our decision to reject the null hypothesis that

the true mean pineapple weight is 31 ounces. In other words, the test and confidence interval lead to the same conclusion about the

null hypothesis but the confidence interval providesmore information: a set of plausible values for the population mean.

INTERPRET THE 95% CONFIDENCE INTERVAL IN CONTEXT. EXPLAIN HOW THE CONFIDENCE INTERVAL LEADS TO THE SAME

CONCLUSION AS THE PREVIOUS EXAMPLE.

95

does not Statistically significant

does Not statistically significant

READ pg. 586-589 Example until the CYU: Is Caffeine Dependence Real?

Then TRY the Supermarket Lanes problem

INFERENCE FOR MEANS: PAIRED DATA

For their second semester project in AP® Statistics, Libby and Kathryn decided to investigate which line was faster in the supermarket: the express lane or a regular lane. To

collect their data, they randomly selected 15 times during a week, went to the same store, and bought the same item. One of the students used the express lane and the other

used the closest regular lane. To decide which lane each of them would use, they flipped a coin. They entered the

lanes at the same time, paid with the same method, and recorded the time in seconds it took them to complete the

transaction.  

Problem: Carry out a test to see if there is convincing evidence that the express lane is faster, on average. Please

note: Use μd when testing differences.

NOW YOU TRY! SUPERMARKET LANES

Because these data are paired, we will consider the differences in time (regular − express). Here are the 15 differences, with a positive difference indicating

that the express lane was faster (took less time).

5 246 −46 121 30 55 79 −94

−17 95 20 14 129 −39 42

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CONCLUDE

READ THE LAST PAGE OF TODAY’S NOTES ON USING TESTS WISELY

DO CHAPTER 9 FRAPPY

RECOMMENDED: CH. 9 AP PRACTICE TEST