AP Statistics

Unit 7 Review- AP Stats

Question 1

A study was conducted to investigate whether the mean price of a dozen eggs was different for two different grocery stores, Store A and Store B, in a large city. A carton of one dozen eggs from each store was randomly selected for each of 35 weeks, for a total sample size of 35 cartons from each store. The mean price of the 35 cartons was recorded for each store. The difference in the mean carton price for the stores will be calculated.

What is the appropriate test for the study?

Multiple Choice

A study was conducted to investigate whether the mean price of a dozen eggs was different for two different grocery stores, Store A and Store B, in a large city. A carton of one dozen eggs from each store was randomly selected for each of 35 weeks, for a total sample size of 35 cartons from each store. The mean price of the 35 cartons was recorded for each store. The difference in the mean carton price for the stores will be calculated.

• A one-sample

  z-test for a population proportion

• A one-sample

  t-test for a sample mean

• A matched-pairs

  t-test for a mean difference

• A two-sample

  t-test for a difference between population means

• A two-sample

  z-test for a difference between population proportions

Question 2

A two-sample t-test for a difference in means was conducted to investigate whether the average time to swim a lap with the freestyle stroke is different from the average time to swim a lap with the butterfly stroke. With all conditions for inference met, the test produced a test statistic of t=−2.073 and

p-value of 0.042.

Based on the p-value and a significance level of

α=0.05, which of the following is a correct conclusion?

Multiple Choice

A two-sample t-test for a difference in means was conducted to investigate whether the average time to swim a lap with the freestyle stroke is different from the average time to swim a lap with the butterfly stroke. With all conditions for inference met, the test produced a test statistic of t=−2.073 and p-value of 0.042.

Based on the p-value and a significance level of α=0.05, which of the following is a correct conclusion?

• There is convincing statistical evidence that the average time to swim a lap with the freestyle stroke is less than the average time to swim a lap with the butterfly stroke.

• There is convincing statistical evidence that the average time to swim a lap with the freestyle stroke is different from the average time to swim a lap with the butterfly stroke.

• There is not convincing statistical evidence that the average time to swim a lap with the freestyle stroke is greater than the average time to swim a lap with the butterfly stroke.

• There is not convincing statistical evidence that the average time to swim a lap with the freestyle stroke is different from the average time to swim a lap with the butterfly stroke.

• There is not convincing statistical evidence that the average time to swim a lap with the freestyle stroke is less than the average time to swim a lap with the butterfly stroke.

Remember!!

If your p-value is less than your alpha value (level of significance), then you reject your null hypothesis (that there is no difference). If you are able to reject your null, then you have evidence to support the alternate hypothesis.

Question 3

A soda manufacturer claims that its Cherry Fizz soda has more carbonation than a competitor’s Cherry Eclipse soda. Bottles of both types of soda are opened, covered with a balloon, and then shaken. The diameter of each balloon is then measured. The mean balloon diameters are 2.3 inches for the Cherry Fizz soda and 2.1 inches for the Cherry Eclipse soda. A 90 percent confidence interval to estimate the difference in mean diameters, in inches, is (−0.8,1.2)

. Which of the following claims is supported by the interval?

Multiple Choice

A soda manufacturer claims that its Cherry Fizz soda has more carbonation than a competitor’s Cherry Eclipse soda. Bottles of both types of soda are opened, covered with a balloon, and then shaken. The diameter of each balloon is then measured. The mean balloon diameters are 2.3 inches for the Cherry Fizz soda and 2.1 inches for the Cherry Eclipse soda. A 90 percent confidence interval to estimate the difference in mean diameters, in inches, is (−0.8,1.2)

. Which of the following claims is supported by the interval?

• Because 2.3 inches is larger than 2.1 inches, the manufacturer is correct, and Cherry Fizz has more carbonation.

• Because the interval has more positive values than negative values, Cherry Fizz has more carbonation.

• Because 2.3 and 2.1 are very similar, there is no difference in the mean carbonation levels.

• The interval cannot be interpreted because negative measurements are not possible.

• Because the interval contains 0, it is possible that there is no difference in mean carbonation levels.

Question 4

The weekly sales at two movie theaters were recorded for a random sample of 25 weeks. A 95 percent confidence interval for the difference in mean weekly sales for the two movie theaters was calculated as ($1,288,$2,586)

.

With all else remaining constant, which of the following would have resulted in a confidence interval narrower than the calculated interval?

Multiple Choice

The weekly sales at two movie theaters were recorded for a random sample of 25 weeks. A 95 percent confidence interval for the difference in mean weekly sales for the two movie theaters was calculated as ($1,288,$2,586)

.

With all else remaining constant, which of the following would have resulted in a confidence interval narrower than the calculated interval?

• A sample size less than 25

• A sample size greater than 25

• An increase to 99 percent confidence

• A sample mean greater than $1,937

• A sample mean less than $1,937

Things to remember about intervals:

• smaller sample size --> wider interval

• larger sample size --> narrower interval

• larger confidence level --> wider interval

• sample mean has no affect on width of interval

Question 5

Which of the following correctly compares the 

t-distribution and z-distribution?

Multiple Choice

Which of the following correctly compares the

t-distribution and

z-distribution?

• For small sample sizes, the density curve of the

  t-distribution is not symmetric, but the density curve of the

  z-distribution is symmetric.

• For large sample sizes, the density curve of the

  t-distribution is not symmetric, but the density curve of the

  z-distribution is symmetric.

• The curves of both distributions are symmetric, but the height of the density curve of the t-distribution is taller than the height of the density curve of the

  z-distribution.

• The area under the density curve of the

  t-distribution is greater than the area under the density curve of the

  z-distribution, especially for small sample sizes.

• The density curve of the

  t-distribution is more spread out than the density curve of the

  z-distribution, especially for small sample sizes.

z dist. vs. t. dist.

The density curve of the 

t-distribution is more spread out than the density curve of the 

z-distribution, especially for small sample sizes.

**Remember, there's more area in the tails of the t-distribution. The z-distribution has more area in the middle

Question 6

A marine biologist wants to estimate the average weight of a population of dolphins living in a certain region of the ocean. The biologist will collect a random sample of dolphins and use the sample weights to create the estimate.

Which of the following is an appropriate method for the biologist to use for inference to the population?

Multiple Choice

A marine biologist wants to estimate the average weight of a population of dolphins living in a certain region of the ocean. The biologist will collect a random sample of dolphins and use the sample weights to create the estimate.

Which of the following is an appropriate method for the biologist to use for inference to the population?

• A one-sample

  t-interval for a population mean

• A one-sample

  t-interval for a sample mean

• A one-sample

  z-interval for a population proportion

• A matched-pairs

  t-interval for a mean difference

• A two-sample

  t-interval for a difference between means

***Remember!! Your inference procedures are always for POPULATIONS

Question 7

To study learned behavior in mice, researchers used a sample of mice in a maze experiment. Each mouse had to find its way through a maze to reach food at the end. The mouse was timed on its first run through the maze and again on its tenth run through the maze. The difference in the times was recorded for each mouse.

Which is the best inference procedure for this scenario?

Multiple Choice

To study learned behavior in mice, researchers used a sample of mice in a maze experiment. Each mouse had to find its way through a maze to reach food at the end. The mouse was timed on its first run through the maze and again on its tenth run through the maze. The difference in the times was recorded for each mouse.

Which is the best inference procedure for this scenario?

• A two-sample

  z-interval for a difference between proportions

• A two-sample

  t-interval for a difference between means

• A matched-pairs

  t-interval for a mean difference

• A one-sample

  z-interval for a population proportion

• A one-sample

  t-interval for a sample mean difference

Matched Pairs

Two observations were recorded for each mouse, the first-run time and the tenth-run time. Since observations are paired for each mouse, the best method is a matched-pairs t

t-interval.

Remember: you use a matched pairs t-test when data points come in pairs- you find a mean of all the paired differences, which then becomes your sample mean

(7.10 DV 1 & 7.5 DV 3)

Question 8

A university researcher wants to estimate the mean number of novels that seniors read during their time in college. An exit survey was conducted with a random sample of 9 seniors. The sample mean was 7 novels with standard deviation 2.29 novels. Assuming that all conditions for conducting inference have been met, which of the following is a 95 percent confidence interval for the population mean number of novels read by all seniors?

Multiple Choice

A university researcher wants to estimate the mean number of novels that seniors read during their time in college. An exit survey was conducted with a random sample of 9 seniors. The sample mean was 7 novels with standard deviation 2.29 novels. Assuming that all conditions for conducting inference have been met, which of the following is a 95 percent confidence interval for the population mean number of novels read by all seniors?

• $$7\pm1.960\left(\frac{2.29}{\sqrt{8}}\right)$$  
  

• $$7\pm1.960\left(\frac{2.29}{\sqrt{9}}\right)$$  

• $$7\pm2.262\left(\frac{2.29}{\sqrt{9}}\right)$$  

• $$7\pm2.306\left(\frac{2.29}{\sqrt{8}}\right)$$  

• $$7\pm2.306\left(\frac{2.29}{\sqrt{9}}\right)$$  

one-sample t interval for a mean

Formula:

 $\overline{x}\pm tstar\left(\frac{s}{\sqrt{n}}\right)$  
To find t*: use inverse t... the confidence level was 95%, so you'd use .025 as the left area and 8 as the d.f. 

Question 9

A team of ecologists will select a random sample of nesting robins in a certain region to estimate the average number of eggs per nest for all robins in the region. Which of the following is a correct inference procedure for the ecologists to use?

Multiple Choice

A team of ecologists will select a random sample of nesting robins in a certain region to estimate the average number of eggs per nest for all robins in the region. Which of the following is a correct inference procedure for the ecologists to use?

• A one-sample

  t-interval for a sample mean

• A one-sample

  t-interval for a population mean

• A one-sample

  z-interval for a population proportion

• A two-sample

  t-interval for a difference between means

• A two-sample

  z-interval for a difference between proportions

Question 10

Animal scientists studied foraging behavior of the scrub lizard, found in central Florida. Foraging is the process of searching for food. To study such behavior, the scientists recorded the number of head movements per minute for a sample of 63 lizards. A 95 percent confidence interval constructed from the sample is given as 

2.7±0.62 head movements per minute.

Based on the interval, is a claim of 3 head movements per minute plausible?

Multiple Choice

Animal scientists studied foraging behavior of the scrub lizard, found in central Florida. Foraging is the process of searching for food. To study such behavior, the scientists recorded the number of head movements per minute for a sample of 63 lizards. A 95 percent confidence interval constructed from the sample is given as 2.7±0.62 head movements per minute.

Based on the interval, is a claim of 3 head movements per minute plausible?

• The claim is not plausible because 3 head movements per minute is contained within the interval.

• The claim is not plausible because 3 head movements per minute is not contained within the interval.

• The claim is not plausible because 95 percent of 3 is greater than the sample mean of 2.7.

• The claim is plausible because 3 head movements per minute is not contained within the interval.

• The claim is plausible because 3 head movements per minute is contained within the interval.

Multiple Choice

The first half of chapter 7, a man did the AP Classroom Daily videos. That man was from the amazing, extraordinary, stunning ___________

• Trenton, New Jersey

• York, Pennsylvania

• Hartford, Connecticut

• Albany, New York

He used many different adjectives to describe beautiful York, Pennsylvania in each video!