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APS22-1 Calculator Work for Proportions

Last updated over 4 years ago
22 questions
Before you start, please be aware that for 1-Prop z-test and intervals for your tests at Franklin, you should show your calculations. On the AP exam, that depends on how much time you have, but you should always show what values you are using (p, p-hat, n, critical values, etc.).

Also, remember that a test will require hypotheses, conditions, and full conclusions in context. This is just focusing on how to do the calculator work and conclusions.
For the next six problems, use the information below.
Is there such thing as a home team advantage? If there is not, the proportion of home games a team wins would be roughly 50%. During the 2006 season, the home team won 136 of the 240 regular-season NFL games.
1

Does this provide evidence that there is a home team advantage? (In other words, is the proportion won significantly greater than 50%)
Find the z-score. To auto-score correctly, round to the nearest thousanth (three decimal places)

1

Does this provide evidence that there is a home team advantage? (In other words, is the proportion won significantly greater than 50%)
Find the P-value. To auto-score correctly, round to the nearest thousanth (three decimal places)

1

Let p= the true proportion of games won by the home team. The null hypothesis would be p=.5. Based on the p-value, and a significance level of .05, we should

1

True or false? This provides evidence of a home team advantage.

1

Create a 95% confidence interval to estimate the true proportion of games won by the home team. Round to three decimal places, don't put any spaces, and use (low,high) for the format of your answer. (FYI- I don't care if there are small differences in rounding, etc. but if you feel better when your answers pop up as correct, follow the instructions carefully)

1

The correct interpretation (conclusion) of this interval is

For the next three problems, use the information below.
Census data for a certain county show that 19% of adult residents are hispanic. Suppose 72 people are called for jury duty and only 9 of them are Hispanic.
1

Does this underrepresentation of Hispanics call into question the fairness of the jury selection system? Run the appropriate test and find the p-value.

1

Based on a significance level of .05, what should you conclude? (this won't auto-grade well, just be sure to read the correct answer carefully)

1

Create a 90% confidence interval to estimate the true proportion of people called for jury duty who are Hispanic.

Hopefully you have read Chapter 22. One of the most difficult parts about 2-proportion procedures is the conclusion, particularly with the confidence intervals. We'll focus more on that during class, and have more practice after we've gone over it. If you struggle with that today, don't panic.
For the next six problems, use the information below.
A survey of 430 randomly chosen adults found that 47 of the 222 men and 37 of the 208 women had purchased books online. Use the hypotheses below.

Where p represents the true proportion who would buys books online. (notice I didn't specify women or men; that's what the sub-w and sub-m are for)
1

Does this provide evidence of a significant difference in the book purchasing habits of men and women? Find the z-score. Round to three decimals.

1

Does this provide evidence of a significant difference in the book purchasing habits of men and women? Find the p-value. Round to three decimals.

1

Based on a significance level of .05, we should...

1

True or false- this provides evidence of a significant difference in the book purchasing habits of men and women.

1

Create a 95% confidence interval to estimate the true difference in the proportion of men and women who would (not "did"- remember we are hypothesising about the parameter, not the statistic) buy books online.

1

The correct interpretation of this interval is:
I'm 95% confident that the true proportion of men who would buy books online is between 4.1% lower and 10.9% higher than the proportion of women who would buy books online.
How does the fact that we have a negative and positive in our confidence interval support our decision from #12? (don't expect this to auto-grade well)

For the remaining problems, use the information below.
In 1998, a San Diego reproductive clinic reported 42 live births to 157 women under the age of 38, but only 7 live births for 89 clients age 38 and older. Does this provide evidence clinic's methods are more successful for women who are under 38? Use the hypotheses below.


Where p= the proportion of pregnancies resulting in live births; group 1- women under age 38 and group 2- women age 38 and older
1

Find the z-score.

1

Find the p-value. Round to five decimals.

1

Based on the p-value, we should conclude...

1

True or false: This provides evidence that the clinic's methods are more successful for women who are under age 38.

1

Create a 95% confidence interval for the true difference in success rates for women under 38 and 38 and older. Round each boundary to four decimals.

1

The correct interpretation of this interval is:
I'm 95% confident the true proportion of pregnancies that result in live birth for women under 38 is between 10% and 28% higher than the proportion for women 38 and older. (normally I wouldn't round to the nearest whole percentage, but rounding up on the low end just comes out that way)

How does this interval support our decision in #18?

1

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