AP Stats Unit 7 FRQ Practice Prompt (#1) Answers & Feedback

FRQ Unit 7 Exam Practice Prompt

FRQ Writing Samples and Feedback

FRQ Practice Submission 1

1. Random - Stated that quality control staff selected random samples of bags
2. 10% Condition for Independence - Safe to assume there are at least 35(10) = 350 bags of chips at the production line
3. Normal/Large Sample Condition - Since n = 35 >= 30, the Normal/Large Sample Condition is satisfied, thus the sampling distribution of x-bar is approximately normal.

No facepalms here! Strong execution in part (a) with your description of a Type II error. In part (b), you execute the test well from start to finish, reaching the appropriate conclusion (which hopefully for the chip manufacturer isn’t a Type II error since we failed to reject Ho!). One little thing: you didn’t address the question of if the line would get shut down (it wouldn’t). Be sure to read the actual question carefully - we might have to connect our conclusion in the hypothesis test to the scenario at hand.

FRQ Practice Submission 2

1. SRS- “random sample of 35 bags of chips” --> stated in the proble
2. independence- 10(35)=350 < population of bags of potato chips
3. normal- 35>30 --> Central Limit Theorem is applied (normal distribution)

In part (a), you correctly describe a type II error and a possible consequence. Be careful with your wording - failing to reject Ho does not necessarily mean we will conclude the mean amount is equal to 10, just that we will not have evidence to conclude that it’s less than 10 oz. (“fail to reject Ho” is not the same as “accept Ho”, and your response makes it sound like we “accept Ho”.)

In part (b), you check the appropriate conditions, but then run a z-test. Z-tests are for proportions (unless we know the population standard deviation, which we don’t) - this should be a “t-test” with a t test statistic. Your p-value and conclusion you get from your z-test are consistent, though, so while you would get partial credit for choosing the test, you would get full credit for your conditions and your conclusion.

FRQ Practice Submission 3

On part (a), you appropriately define a type II error in this context. Your sentence about the possible consequence only really needs to list one reason (“identify A possible consequence”), so be sure to fully explain just your one. For example, in this case you could say “This may lead to customer dissatisfaction because they will be getting less than the advertised amount” or “this means that the manufacturer will not fix the machine that is broken and needs to be fixed.”

FRQ Practice Submission 4

1. We have a random sample of bags of chips.
2. Population of chips is at least 350
3. Since n is large enough due to CLT, the sampling distribution is approximately normal.
4. Standard deviation is known

Nicely done! You give a clear and in-context description of the Error in part (a), and do all appropriate steps in part (b).

FRQ Practice Submission 5

1. random: question states they took “a random sample”
2. normal: sample size is greater than 30, (35>30), so according to the CLT, we can assume normality.
3. independence: we can assume there are greater than 35(10) 350 bags of chips in the whole population so the independence condition is met.

Nice work on both parts - in part (a) you appropriate define a Type II error in this context and give a reasonable consequence. In part (b) you name the appropriate test, check conditions, and execute correctly including the correct decision based on the p-value, stated in context.

FRQ Practice Submission 6

1. Random: We were told the sample was randomly selected.
2. Normal: The sampling distribution is approximately normal because n>=30 (35>30) 
3. 10% Condition: There are more than 10×35 bags of chips on the production line.

• tTest(µ0=10, x¯=9.9, Sx=0.45, n=35)=-1.31468
• p-value=0.098708

Excellent work on the hypothesis test in part (b) [shout out to the copy-paste of the parameters and hypotheses!]. Be careful in your description of part (a). You mention that a Type II error is when we fail to reject Ho… but that is not the same as accepting Ha. We should never use the word “accept” when talking about Ho or Ha. We either reject/fail to reject Ho, and find evidence for/don’t find evidence for Ha. So a Type II error is when we fail to reject Ho when Ha is really true, so we should find evidence for it. Furthermore, you don’t mention the mean in your description (it’s not that each individual bag of chips would have less than 10 oz, it’s that the mean would be less than 10 oz). With the incomplete description of the Type II error (but correct description of the consequence), you would likely earn partial credit for part (a).

FRQ Practice Submission 7

1. Random: It is given that the manufactures selects it at random
2. 10%: 35 bags <= 10% of all the bags produced at the line (most likely). Since we have satisfied these conditions, we can assume independence for the chips bags
3. Normality: Since n>30 (35>30), this condition is satisfied. Since normality is satisfied, we can assume the sample is large enough.

Solid work! Be careful when you say “retain the null.” That almost makes it sound like you’re accepting the null hypothesis, which we don’t do. Safer to say “fail to reject the null” or “do not reject the null.” Your work in part (b) has all appropriate components. In part (a), you would probably only get partial credit, because you never mention that we’re dealing with the mean amount in the chip bags, not the amounts in individual chip bags. So we should say “the bags contain a mean of 10 ounces of chips when in reality the production line has a mean of less than 10 ounces”, or something similar.

FRQ Practice Submission 8

1. Random: We are told they are using a “random sample of 35 bags of chips”
2. Normal: It is normal because 35>30
3. 10% condition: There are more than 35 x 10 bags of chips in the production lines

In part (a), you demonstrate an understanding of Type II errors but do not quite explain this context properly. The hypothesis test isn’t about whether each bag has 10 chips (as you imply), it’s about whether the mean weight in the bags is 10 ounces. So individual bags may very well have 10 ounces, as they are supposed to, but the overall average may be lower than that due to bags with less. In part b, you appropriately conduct the test and reach the correct conclusion.

FRQ Practice Submission 9

1. Random: “In a random sample of 35 bags of chips”
2. Normal: Because 35 ≥ 30, the data is approximately normal
3. Independent: It is reasonable to assume that the population of the potato chip bags produced by the manufacturer is at least 350.

Nice work on both parts - you describe a Type II error using appropriate context, and conduct an appropriate hypothesis test in part b, reaching the correct conclusion.

FRQ Practice Submission 10

Good work! In part (a) you appropriately define a Type II error in this context; in part (b) you execute the hypothesis test appropriately