6.13 MC Answers and Review

⛔STOP ⛔ Before you look at the answers make sure you gave this practice quiz a try so you can assess your understanding of the concepts covered in Unit 6. Click here for the practice questions: AP Statistics Unit 6 Multiple Choice Questions.

Facts about the test: The AP Statistics exam has 40 multiple choice questions and you will be given 1 hour 30 minutes to complete the section. That means it should take you around 11 minutes to complete 5 questions.

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B. 1 Proportion T Interval

C. 1 Proportion Z Test

D. 1 Sample T Interval

Answer: A 1 proportion z interval (or 1PropZInt for calculator speak) is the appropriate procedure for estimating a proportion. Remember, proportions always use z scores!

A. Randomness

B. 10% Condition

D. Large Counts Condition

Answer: Central Limit Theorem is NOT applicable for proportions. We use the large counts condition when verifying that our sampling distribution is normal.

A. 0.6

C. 0.3

D. 0.45

Answer: The margin of error is our "buffer zone" that we add and subtract to our point estimate. In this example, our point estimate is 0.45, and therefore we added and subtracted 0.15 to get our endpoints for our confidence interval.

A. 0.9

B. 0.1

C. 0.75

Answer: When determining the minimum sample size for a given margin of error, always use a p-hat of 0.5. Since your standard error is multiplying p and (1-p), using a p of 0.5 will maximize our standard error and therefore gives us the "worst case scenario" to determine our minimum sample size to get a given margin of error, regardless of our p-hat.

A. It increases

C. It stays the same

D. Not enough information to determine

Answer: As the sample size increases, this will decrease our standard error. Therefore, our margin of error will also decrease.

A. Ho: p<0.2

B. Ho: p-hat=0.2

D. Ho: p>0.2

Answer: Our null hypothesis is always a claim about the population proportion, so it is referring to a p, not a p-hat. Also, our null claim is always an equivalence statement, not an inequality.

B. There is a 92% chance that the confidence interval is correct.

C. There has been 92 confidence intervals selected and the middle one of those is the one used for the study.

D. Among 92% of the people interviewed, they fell within the given confidence interval.

Answer: The confidence level reflects the percentage of possible confidence intervals from the given population that would contain the true proportion. It is important to note that this is out of many, many samples AND they are drawn from the same population,

B. 0.04

C. 0.6

D. 1

Answer: The lower the p-value, the further our sample is from the mean of our sampling distribution, therefore, the rarer it is. If it is extremely rare, this leads us to doubt the claimed mean of our sampling distribution.

A. Fail to reject, should

B. Accept, shouldn't

D. Reject, should

Answer: A type I error is when we reject the null hypothesis and the correct decision would have been to fail to reject the null hypothesis because the Ho was true. In order to remember our type I/II error, remember that a type TWO error is when we fail TO reject the null but we should have rejected. Therefore, a type I error is the opposite: we rejected and shouldn't have. Also "reject" is one word: Type 1.

A. It increases

C. It stays the same

D. Not enough information to tell

Answer: As our confidence level decreases, the area of the tail for our z interval decreases. Therefore, the z score decreases, and in turn, our margin of error decreases.

A. There is a 0.023 chance of rejecting the null hypothesis.

C. The true population proportion is 0.023.

D. The probability of obtaining the proportion in the null hypothesis exactly is 0.023.

Answer: When performing a hypothesis test, we always assume the null. Now that we have assumed the null, the p-value is the probability of obtaining our exact random sample that we have hard proof of.

A. Since 0.023<0.05, we accept the null hypothesis. There is evidence that the null is true.

B. Since 0.023<0.05, we fail to reject the Ha. There is convincing evidence of our Ha.

C. Since 0.023<0.05, we accept the Ha. There is evidence of the Ha.

Answer: The first sentence of our conclusion should always be in reference to the Ho. The second sentence should be in reference to the Ha. We NEVER accept either of the two. We either reject or fail to reject.

A. 0.32

B. 0.64

C. 0.4

Answer: To find the probability of making a type 2 error, take the power and subtract from one.

A. 1 Prop Z interval

B. 2 Sample T-Test

D. Test for Linear Regression

Answer: A randomized experiment with two treatments would be best using either a 2 Prop Z Interval or 2 Prop Z Test.

A. (-0.05, 0.1)

B. (-0.1,0.3)

D. (-0.02, 0.13)

Answer: Since 0 is not contained in the correct interval, that means that our p-value would be less than 0.05 (1-0.95) and we would therefore reject the null hypothesis.

📄 Study AP Statistics, Unit 6.8: Confidence Intervals for the Difference of Two Proportions

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