Question

Cherries – The Cherry Hill Growers Association operates a fruit warehouse in California. Because of the volume of cherries that arrive at the warehouse during picking season, the growers have agreed that instead of weighing each box of cherries, they would assume that a fully filled box of cherries weighs 15 pounds, on average. Past studies have shown that the standard deviation of weight from box to box is 0.55 pound. Jeremiah is the manager of the warehouse. He wants to guard against purchasing boxes of cherries from growers who underfill the boxes. He is not concerned if the boxes are overfilled. Each time a grower brings a delivery of cherry boxes, Jeremiah uses the following decision rule: He selects a random sample of 14 boxes of cherries from the delivery and if the mean weight of the 14 boxes is less than 14.56 pounds, Jeremiah will not purchase any cherries from that delivery. Round all calculated values to 4 decimal places. Use a null and alternative hypothesis of H0 : ? = 15 vs. Ha : ? < 15. 1. Which of the following describes a Type I error in this situation? A. Jeremiah does not purchase cherries from this grower when the grower's boxes are underfilled. B. Jeremiah purchases the cherries from this grower when the grower's boxes are underfilled. C. Jeremiah does not purchase cherries from this grower when the grower's boxes are not underfilled. D. Jeremiah purchases the cherries from this grower when the grower's boxes are not underfilled. 2. Which of the following describes a Type II error in this situation? A. Jeremiah does not purchase cherries from this grower when the grower's boxes are not underfilled. B. Jeremiah purchases the cherries from this grower when the grower's boxes are not underfilled. C. Jeremiah purchases the cherries from this grower when the grower's boxes are underfilled. D. Jeremiah does not purchase cherries from this grower when the grower's boxes are underfilled. 3. What is the probability that Jeremiah will make a Type I error with this decision rule? Probability of a Type I error = 4. Using the decision rule, what is the power of the hypothesis test if the mean weight of the grower's boxes is actually 14.77 pounds? Power = 5. Jeremiah wonders what will happen to the Type I error rate if he changes the sample size. Suppose that instead of 14 boxes, he randomly samples 15 boxes. Will the change cause the Type I error rate to increase, decrease, or stay the same? A. Increase B. Decrease C. Stay the same

Cherries – The Cherry Hill Growers Association operates a fruit warehouse in California. Because of the volume of cherries that arrive at the warehouse during picking season, the growers have agreed that instead of weighing each box of cherries, they would assume that a fully filled box of cherries weighs 15 pounds, on average. Past studies have shown that the standard deviation of weight from box to box is 0.55 pound.

Jeremiah is the manager of the warehouse. He wants to guard against purchasing boxes of cherries from growers who underfill the boxes. He is not concerned if the boxes are overfilled.

Each time a grower brings a delivery of cherry boxes, Jeremiah uses the following decision rule: He selects a random sample of 14 boxes of cherries from the delivery and if the mean weight of the 14 boxes is less than 14.56 pounds, Jeremiah will not purchase any cherries from that delivery.

Round all calculated values to 4 decimal places.

Use a null and alternative hypothesis of
H0 : ? = 15 vs. Ha : ? < 15.

1. Which of the following describes a Type I error in this situation?
A. Jeremiah does not purchase cherries from this grower when the grower's boxes are underfilled.
B. Jeremiah purchases the cherries from this grower when the grower's boxes are underfilled.
C. Jeremiah does not purchase cherries from this grower when the grower's boxes are not underfilled.
D. Jeremiah purchases the cherries from this grower when the grower's boxes are not underfilled.

2. Which of the following describes a Type II error in this situation?
A. Jeremiah does not purchase cherries from this grower when the grower's boxes are not underfilled.
B. Jeremiah purchases the cherries from this grower when the grower's boxes are not underfilled.
C. Jeremiah purchases the cherries from this grower when the grower's boxes are underfilled.
D. Jeremiah does not purchase cherries from this grower when the grower's boxes are underfilled.

3. What is the probability that Jeremiah will make a Type I error with this decision rule?
Probability of a Type I error =

4. Using the decision rule, what is the power of the hypothesis test if the mean weight of the grower's boxes is actually 14.77 pounds?
Power =

5. Jeremiah wonders what will happen to the Type I error rate if he changes the sample size. Suppose that instead of 14 boxes, he randomly samples 15 boxes. Will the change cause the Type I error rate to increase, decrease, or stay the same?
A. Increase
B. Decrease
C. Stay the same

Cherries – The Cherry Hill Growers Association operates a fruit warehouse in California. Because of the volume of cherries that arrive at the warehouse during picking season, the growers have agreed that instead of weighing each box of cherries, they would assume that a fully filled box of cherries weighs 15 pounds, on average. Past studies have shown that the standard deviation of weight from box to box is 0.55 pound.

Jeremiah is the manager of the warehouse. He wants to guard against purchasing boxes of cherries from growers who underfill the boxes. He is not concerned if the boxes are overfilled.

Each time a grower brings a delivery of cherry boxes, Jeremiah uses the following decision rule: He selects a random sample of 14 boxes of cherries from the delivery and if the mean weight of the 14 boxes is less than 14.56 pounds, Jeremiah will not purchase any cherries from that delivery.

Round all calculated values to 4 decimal places.

Use a null and alternative hypothesis of
H0 : ? = 15 vs. Ha : ? < 15.

1. Which of the following describes a Type I error in this situation?
A. Jeremiah does not purchase cherries from this grower when the grower's boxes are underfilled.
B. Jeremiah purchases the cherries from this grower when the grower's boxes are underfilled.
C. Jeremiah does not purchase cherries from this grower when the grower's boxes are not underfilled.
D. Jeremiah purchases the cherries from this grower when the grower's boxes are not underfilled.

2. Which of the following describes a Type II error in this situation?
A. Jeremiah does not purchase cherries from this grower when the grower's boxes are not underfilled.
B. Jeremiah purchases the cherries from this grower when the grower's boxes are not underfilled.
C. Jeremiah purchases the cherries from this grower when the grower's boxes are underfilled.
D. Jeremiah does not purchase cherries from this grower when the grower's boxes are underfilled.

3. What is the probability that Jeremiah will make a Type I error with this decision rule?
Probability of a Type I error =

4. Using the decision rule, what is the power of the hypothesis test if the mean weight of the grower's boxes is actually 14.77 pounds?
Power =

5. Jeremiah wonders what will happen to the Type I error rate if he changes the sample size. Suppose that instead of 14 boxes, he randomly samples 15 boxes. Will the change cause the Type I error rate to increase, decrease, or stay the same?
A. Increase
B. Decrease
C. Stay the same

Added by Justin P.

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