Lesson 9.6 Checkpoint

For high school students who can leave campus for lunch, "Go in or drive-thru?" is a very important question. Ben and Maya decided to investigate by visiting a local fast-food restaurant on 10 randomly selected days during lunch. Each time they went, they flipped a coin to determine which of them would go inside and which would use the drive-thru. Both of them ordered the same item, paid with the same amount of cash, and recorded how long it took (in seconds) to wait in line, pay, and receive their item. Here are their data.

Do these data provide convincing evidence at the α = 0.05 level of a mean difference in the service time inside and at the drive-thru for this local fast- food restaurant?

Which of the following is appropriate STATE for this problem?

(LT 9.6.1 #1)

• We want to perform a test at α = 0.05 level of

  H₀: μ₁ - μ₂ = 0

  H_a: μ₁ - μ₂ ≠ 0

  where μ₁ = the true mean drive-thru service time in seconds for local fast-food restaurant and μ₂ = the true mean inside service time in seconds for local fast-food restaurant.

• We want to perform a test at α = 0.05 level of

  H₀: μ₁ - μ₂ = 0

  H_a: μ₁ - μ₂ ≠ 0

  where μ₁ = the true mean inside service time in seconds for local fast-food restaurant and μ₂ = the true mean drive-thru service time in seconds for local fast-food restaurant.

• We want to perform a test at α = 0.05 level of

  H₀: μ_diff= 0

  H_a: μ_diff ≠ 0

  where μ_diff = the true mean difference (Drive-thru - Inside) in service times in seconds for local fast-food restaurant.

• We want to perform a test at α = 0.05 level of

  H₀: μ_diff= 0

  H_a: μ_diff ≠ 0

  where μ_diff = the true mean difference (Inside - Drive-Thru) in service times in seconds for local fast-food restaurant.

For high school students who can leave campus for lunch, "Go in or drive-thru?" is a very important question. Ben and Maya decided to investigate by visiting a local fast-food restaurant on 10 randomly selected days during lunch. Each time they went, they flipped a coin to determine which of them would go inside and which would use the drive-thru. Both of them ordered the same item, paid with the same amount of cash, and recorded how long it took (in seconds) to wait in line, pay, and receive their item. Here are their data.

Do these data provide convincing evidence at the α = 0.05 level of a mean difference in the service time inside and at the drive-thru for this local fast- food restaurant?

Which of the following is appropriate Inference Method for this problem?

(LT 9.6.2 #1)

• One-Sample t Test for μ_diff

• Two-Sample t Test for μ₁ - μ₂

• One-Sample t Test for μ₁ - μ₂

• Two-Sample t Test for μ_diff

For high school students who can leave campus for lunch, "Go in or drive-thru?" is a very important question. Ben and Maya decided to investigate by visiting a local fast-food restaurant on 10 randomly selected days during lunch. Each time they went, they flipped a coin to determine which of them would go inside and which would use the drive-thru. Both of them ordered the same item, paid with the same amount of cash, and recorded how long it took (in seconds) to wait in line, pay, and receive their item. Here are their data.

Do these data provide convincing evidence at the α = 0.05 level of a mean difference in the service time inside and at the drive-thru for this local fast- food restaurant?

Which of the following are the correct t and P-value?

(LT 9.6.1 #2)

• t = 4.417 , P-value = 0.0017

• t = -4.417 , P-value = 0.0017

• t = -4.417 , P-value = 0.9992

• t = 4.417 , P-value = 0.9992

For high school students who can leave campus for lunch, "Go in or drive-thru?" is a very important question. Ben and Maya decided to investigate by visiting a local fast-food restaurant on 10 randomly selected days during lunch. Each time they went, they flipped a coin to determine which of them would go inside and which would use the drive-thru. Both of them ordered the same item, paid with the same amount of cash, and recorded how long it took (in seconds) to wait in line, pay, and receive their item. Here are their data.

Do these data provide convincing evidence at the α = 0.05 level of a mean difference in the service time inside and at the drive-thru for this local fast- food restaurant?

Which of the following are the correct CONCLUDE?

(LT 9.6.1 #3)

• Because the P-value of 0.0017 is less than α = 0.05, we reject H₀. There is convincing evidence of a difference in the average service time inside and at the drive-thru for this local fast-food restaurant.

• Because the P-value of 0.0017 is less than α = 0.05, we fail to reject H₀. There isn't convincing evidence of a difference in the average service time inside and at the drive-thru for this local fast-food restaurant.

• Because the P-value of 0.9992 is greater than α = 0.05, we fail to reject H₀. There isn't convincing evidence of a difference in the average service time inside and at the drive-thru for this local fast-food restaurant.

• Because the P-value of 0.9992 is greater than α = 0.05, we reject H₀. There is convincing evidence of a difference in the average service time inside and at the drive-thru for this local fast-food restaurant.

To compare the wear characteristics of two tire brands, two new Brand A tires are mounted on one side of each of 30 cars of the same model, while two new Brand B tires are mounted on the other side. Which side gets which brand is determined by flipping a coin. After 5000 miles of driving, the amount of wear is measured for each tire.

Decide whether you should use two-sample t procedures to perform inference about a difference in means or one-sample t procedures to perform inference about a mean difference. Explain.

(LT 9.6.2 #2)

• One-sample t procedures; the data come from a matched pairs experiment with the two treatments (tire Brand A and tire Brand B) being randomly assigned to the left and right side of each car.

• Two-sample t procedures; the data come from a matched pairs experiment with the two treatments (tire Brand A and tire Brand B) being randomly assigned to the left and right side of each car.

• One-sample t procedures; the data come from two groups in a randomized experiment with the two treatments (tire Brand A and tire Brand B) being randomly assigned to the left and right side of each car.

• Two-sample t procedures; the data come from two groups in a randomized experiment with the two treatments (tire Brand A and tire Brand B) being randomly assigned to the left and right side of each car.

To compare funding for men’s and women’s sports teams, researchers randomly select 100 colleges and record the amount of money spent on the men’s basketball program and the women’s basketball program at each college.

Decide whether you should use two-sample t procedures to perform inference about a difference in means or one-sample t procedures to perform inference about a mean difference. Explain.

(LT 9.6.2 #3)

• One-sample t procedures; the data are paired by college, and they come from a random sample of 100 colleges.

• Two-sample t procedures; the data are paired by college, and they come from a random sample of 100 colleges.

• One-sample t procedures; they come from two separate random sample of 100 colleges.

• Two-sample t procedures; they come from two separate random sample of 100 colleges.