Answers CA-Statistics and Probability BIntroduction to Hypothesis Testing

Introduction to Hypothesis Testing Answers

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A study found that 15% of teenagers get the recommended 8 to 10 hours of sleep each school night. A guidance counselor at a large high school takes a random sample of 80 students and asks them if they get 8 to 10 hours of sleep each night of the school week. Of the 80 students, 15 state they get 8 to 10 hours of sleep each school night. The P-value for the test of the hypotheses, H0:p=0.15 and Ha:p≠0.15, is 0.35.What is the correct interpretation of this value?

If 15% of teenagers get 8 to 10 hours of sleep each school night, there is a 35% probability that the sample proportion would be 0.19 or more different by chance alone.

Assuming 15% of teenagers get the recommended 8 to 10 hours of sleep each school night, there is a 35% chance that the sample proportion would be 0.19 by chance alone.

If 15% of teenagers get the recommended 8 to 10 hours of sleep each school night, then 35% of the teenagers in this sample got the recommended amount of sleep by chance alone.

Assuming 15% of teenagers get the recommended 8 to 10 hours of sleep each school night, there is a 35% chance that the true proportion of teenagers getting the recommended sleep is 0.15 by chance alone.

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A popular restaurant chain will open a new franchise if a study shows that more than 60% of residents in an area would purchase food from the restaurant. An analyst of a particular area randomly selects 500 residents and surveys them about their interest in the restaurant. Of the 500 residents, 320 stated they would purchase food from the restaurant. Which hypotheses test the proportion of residents who would purchase food from the restaurant in this area?

H 0: p = 0.64, H alpha: p less-than 0.64

H 0: p = 0.60, H alpha: p less-than 0.60

H 0: p = 0.64, H alpha: p greater-than 0.64

H 0: p = 0.60, H alpha: p greater-than 0.60

A statistics student believes that black cars are less likely to receive tickets for moving violations. Black cars make up 19% of all cars manufactured. The student randomly selects 70 moving violation records and finds that 10 of them involved black cars. The P-value for the test of the hypotheses, . What is the correct interpretation of this value?

There is a 24% chance of a black car receiving a moving violation.

Assuming the true proportion of black cars that receive moving violations is 0.19, there is a 24% probability that the null hypothesis is true.

Assuming the true proportion of black cars that receive moving violations is 0.19, there is a 24% probability that the sample proportion would be 0.15 or less by chance alone.

Assuming the true proportion of black cars that receive moving violations is less than 0.19, there is a 24% probability that the sample proportion would be 0.15 or less by chance alone.

A popular restaurant chain will open a new franchise if a study shows that more than 60% of residents in an area would purchase food from the restaurant. An analyst of a particular area randomly selects 500 residents and surveys them about their interest in the restaurant. Of the 500 residents, 320 stated they would purchase food from the restaurant. The P-value for the test of the hypotheses, and , is 0.03. What is the correct conclusion given ?

Because the P-value is less than , the analyst should reject H0.

Because the P-value is less than , the analyst should fail to reject H0.

Because the P-value is greater than , the analyst should reject H0.

Because the P-value is greater than , the analyst should fail to reject H0.

When spinning a penny, Claire believes the proportion of times the penny lands on heads is higher than 0.5. She spins a penny 50 times and it lands on heads 32 times. The P-value for the test of the hypotheses, and , is 0.02. What is the correct conclusion given ?

Because the P-value is less than , Claire should reject H0.

Because the P-value is less than , Claire should fail to reject H0.

Because the P-value is greater than , Claire should reject H0.

Because the P-value is greater than , Claire should fail to reject H0.

A local school board wants to determine if the proportion of households in the district that would support starting the school year a week earlier has changed from the previous year. Last year, the school board determined that 65% of households supported starting school earlier. They ask a random sample of 100 households this year, and 70% state they would support starting the school year earlier. Which hypotheses would determine if the proportion of households that support starting school earlier has changed this year?

H 0: p = 0.65, H alpha: p not-equals 0.65

H 0: p = 0.65, H alpha: p greater-than 0.65

H 0: p = 0.70, H alpha: p not-equals 0.70

H 0: p not-equals 0.70, H alpha: p = 0.70

A study found that 15% of teenagers get the recommended 8 to10 hours of sleep each night. A guidance counselor at a large high school takes a random sample of 80 students and asks them if they get 8 to 10 hours of sleep each night of the school week. Of the 80 students, 15 state they get 8–10 hours of sleep each school night. Which hypotheses would test if the proportion of students at this high school is different from the proportion in the study?

H0:p ≠ 0.19, Ha:p = 0.19

H0:p ≠ 0.15, Ha:p = 0.15

H0:p = 0.19, Ha:p ≠ 0.19

H0:p = 0.15, Ha:p ≠ 0.15

A study found that 80% of teenagers use social media on a regular basis. John wanted to investigate if the proportion of students at his large high school who use social media is different. He takes a random sample of 90 students and finds that 64 of them use social media on a regular basis. The P-value for the test of the hypotheses, is 0.035. What is the correct interpretation of this value?

Only 3.5% of teenagers in this sample use social media.

Assuming 80% of teenagers use social media, there is a 0.035 probability of getting a sample proportion of 0.71 or more that is different from 0.8.

Assuming 80% or more teenagers use social media, there is a 0.035 probability of getting a sample proportion of 0.71 or more that is different from 0.8.

Assuming this sample was collected correctly, the probability of getting 64 teenagers out of 90 who use social media is 0.035 if 80% of teenagers use social media.

A computer company wants to determine if the proportion of defective computer chips from a day’s production is more than 10%. A quality control specialist randomly selects 200 chips from a day’s production and finds that 30 chips are defective. The P-value for the test of the hypotheses, and , is 0.009. What is the correct interpretation of this value?

There is a 0.9% chance that the true proportion is 0.10.

There is a 0.9% chance of getting a sample proportion of 0.15 or greater by chance alone if 0.10 is the true proportion.

Assuming 0.10 is the true proportion of defective computer chips, this sample proportion, 0.15, can be expected by chance 0.9% of the time.

Assuming the sample proportion of defective computer chips is 0.15 or more, there is a 0.9% chance that the true proportion of defective computer chips is 0.10.

A teacher has a large container of blue, red, and green beads. She reports to the students that the proportion of blue beads in the container is 0.30. The students feel the proportion of blue beads is lower than 0.30. A student randomly selects 50 beads and finds that 12 of the beads are blue. Which hypotheses would test the students’ claim?

H 0: p = 0.30, H alpha: p greater-than 0.30

H 0: p = 0.30, H alpha: p less-than 0.30

H 0: p = 0.30, H alpha: p not-equals 0.30

H 0: p = 0.24, H alpha: p less-than 0.24

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Introduction to Hypothesis Testing Answers

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