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Chapter 7: Q.AP2.22 - Cumulative AP Practise Test (page 438)

A health worker is interested in determining if omega-3 fish oil can help reduce cholesterol in adults. She obtains permission to examine the health records of 200 people in a large medical clinic and classifies them according to whether or not they take omega-3 fish oil. She also obtains their latest cholesterol readings and finds that the mean cholesterol reading for those who are taking omega-3 fish oil is 18 points less than the mean for the group not taking omega-3 fish oil.

a. Is this an observational study or an experiment? Justify your answer.

b. Explain the concept of confounding in the context of this study and give one example of a variable that could be confounded with whether or not people take omega-3 fish oil.

c. Researchers find that the 18-point difference in the mean cholesterol readings of the two groups is statistically significant. Can they conclude that omega-3 fish oil is the cause? Why or why not?

Short Answer

Expert verified

(a) the no treatment was assigned, the study is an observational study.

(b) the amount of exercise also affects of the amount of exercise is confounded with the omega-3 fish oil.

(c) the omega-3 fish oil is the reason of the statistically significant difference.

Step by step solution

01

Part (a) Step 1: Given Information

Observational study

02

Part (a) Step 2: Simplification

An experiment deliberately forces some treatment on individuals in arrangement to detect their responses. An observational study tries to store information without disturbing the scene they are noticing. The subjects were not given any treatment due to the data being based on health records and therefore the researchers had no control over who took and who did not take omega-3 fish oil. If the no treatment was assigned, the study is an observational study.

03

Part (b) Step 1: Given Information

Two variables are confounded if their affect on a response variable cannot be discriminated from each other. The amount of exercise is a possible confounding variable.

04

Part (b) Step 2: Simplification

Two variables are confounded when their affected on a response variable cannot be discriminated from each other. People who take omega-3 fish oil may be more interested in having a good health and therefore these people may exercise more. Although, the amount of exercise also affects of the amount of exercise is confounded with the omega-3 fish oil.

05

Part (c) Step 1: Given Information

because there are possible confounding variables

06

Part (c) Step 2: Simplification

The conclusion from the previous part is that the study would be an observational study and that the study had possible confounding variables. As long as there are possible confounding variables which cannot be 100%assure that the omega-3 fish oil is the reason of the statistically significant difference.

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Most popular questions from this chapter

Lightning strikes The number of lightning strikes on a square kilometer of open ground in a year has mean 6 and standard deviation 2.4. The National Lightning Detection Network (NLDN) uses automatic sensors to watch for lightning in 1-square-kilometer plots of land. Find the probability that the total number of lightning strikes in a random sample of 50 square-kilometer plots of land is less than 250.

The number of unbroken charcoal briquets in a 20-pound bag filled at the factory follows a Normal distribution with a mean of 450 briquets and a standard deviation of 20 briquets. The company expects that a certain number of the bags will be underfilled, so the company will replace for free the 5%of bags that have too few briquets. What is

the minimum number of unbroken briquets the bag would have to contain for the company to avoid having to replace the bag for free?

a. 404

b. 411

c. 418

d. 425

e. 448

According to the U.S. Census, the proportion of adults in a certain county who owned their own home was 0.71. An SRS of 100 adults in a certain section of the county found that 65 owned their home. Which one of the following represents the approximate probability of obtaining a sample of 100 adults in which 65 or fewer own their home, assuming that this section of the county has the same overall proportion of adults who own their home as does the entire county?

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b. (10065)(0.29)65(0.71)3510065(0.29)65(0.71)35

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P(z鈮�0.65-0.71(0.71)(0.29)100)Pz鈮�0.65-0.71(0.71)(0.29)100

d.P(z鈮�0.65-0.71(0.65)(0.35)100)Pz鈮�0.65-0.71(0.65)(0.35)100

e.P(z鈮�0.65-0.71(0.71)(0.29)100)Pz鈮�0.65-0.71(0.71)(0.29)100

The central limit theorem is important in statistics because it allows us to use a Normal distribution to find probabilities involving the sample mean if the

a. sample size is reasonably large (for any population).

b. population is Normally distributed (for any sample size).

c. population is Normally distributed and the sample size is reasonably large.

d. population is Normally distributed and the population standard deviation is known (for any sample size).

e. population size is reasonably large (whether the population distribution is known or not).

A study of rush-hour traffic in San Francisco counts the number of people in each car entering a freeway at a suburban interchange. Suppose that this count has mean 1.6 and standard deviation 0.75 in the population of all cars that enter at this interchange during rush hour.

a. Without doing any calculations, explain which event is more likely:

  • randomly selecting 1 car entering this interchange during rush hour and finding 2 or more people in the car
  • randomly selecting 35 cars entering this interchange during rush hour and finding an average of 2 or more people in the cars

b. Explain why you cannot use a Normal distribution to calculate the probability of the first event in part (a).

c. Calculate the probability of the second event in part (a).
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