7.12 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 7. Click here for the practice questions: AP Statistics Unit 7 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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A. n

C. n/2

D. 2n

Answer: To find the degrees of freedom, subtract one from the sample size. Degrees of freedom refers to how many chosen for your sample are free to be whatever they please and still get the given population mean. For instance, if the population mean is 10 and our sample size is 5, the first 4 we choose for our sample can be basically whatever they want. However, the last one would be fixed (AKA not free) in order to get the mean of 10.

B. 2 Sample T

C. 1 Proportion T

D. 2 Sample Z

Answer: Since it is a matched pair experiment, every subject received both treatments. Therefore, we can subtract the average for each subject and it essentially becomes one sample using the differences. Since we are estimating a mean, we use a t interval.

A. Sample plot shows no skewness or outliers.

B. Population is normally distributed

C. Sample size of at least 30

Answer: The size of our sample mean does not determine shape at all. However, sample size does (Central Limit Theorem) along with a normal population or a fairly symmetric sample distribution.

A. 95% of giraffes weigh between 1600 and 2000 pounds.

B. There is a 95% probability that a giraffe weighs between 1600 and 2000 pounds.

D. There is only a 5% chance of selecting a giraffe that weighs outside of 1600 and 2000 pounds.

Answer: The correct interpretation is more so about the interval, not the population mean. We are that sure that the confidence interval we have contains the true mean. This is a good template to learn and be familiar with.

B. When the sample size is at least 100

C. When we know the sample mean

D. When the sample is 10% of our population

Answer: In the rare occasion that the population standard deviation is known, one can use a z interval instead of a t interval to estimate a population mean. However, this is pretty rare since this would usually mean you know the population mean (in which case it would be pointless to try to estimate something that you already know)

A. The width increases

C. The width does not change with sample size.

D. Not enough information to determine.

Answer: Since the sample size increasing will decrease our standard error, our margin of error decreases as well. A decreased margin of error means our confidence interval becomes more narrow.

A. z score

C. chi square score

D. p-value

Answer: Any inferential procedure using means will use a t score as its critical value or test statistic.

B. p-value >0.05

C. t score <0.05

D. t score>0.05

Answer: When comparing with the α level, in order to reject our null hypothesis, we need a p-value less than our α. A decision can be made using the t score, but we are typically looking for an extreme test statistic (far away from 0) and 0.05 as a test statistic would not be unlikely.

A. Ho: μ<55

B. Ho: x-bar=55

D. Ho: x-bar<55

Answer: Our null hypothesis is always a claim about the population mean (μ) and our null hypothesis is always an equality statement.

A. confidence level

B. sample size

C. sample mean

Answer: Our critical value takes two things into consideration: degrees of freedom and confidence level. Since we are using the family of t distributions here, our critical value changes as our sample size changes (which changes the degrees of freedom). Also, our confidence level changing adjusts our critical value because it affects what the middle area is of our t distribution.

A. 21

C. 17

D. 14

Answer: To find the point estimate when given a confidence interval, you are finding the midpoint of the interval. Add the two bounds and divide by 2 to take the average of the upper and lower bounds.

A. 1.658

C. 2.576

D. 1.96

Answer: To find the t score, you would take the tail probability (0.005) and our df (39) and enter it into invT function in your calculator. Be careful not to make the mistake of selecting the z score for a 99% confidence interval.

B. 0.05

C. 0.03

D. 0.01

Answer: Since our p value is less than 0.1, it must also be less than 0.15, but we do not know for certain that it is less than 0.05, 0.01 or 0.03.

A. Statistical Fallacy

B. Type 1 error

C. Type 3 error

Answer: When we fail TO reject and we should have, this is a type TWO error.

A. 0.1

B. 0.95

D. 0.5

Answer: The probability of committing a type 1 error is the same as the significance level. A type 1 error is made when we reject the null erroneously. We reject the null when the p-value is less than 0.05. Basically, there is a 0.05 chance of getting that p-value by random chance, hence a 5% probability of rejecting the null based on rare chance.

📄 Study AP Statistics, Unit 7.1: Introducing Statistics: Should I Worry About Error?

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