Introduction to Hypothesis Testing quiz

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?

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.

A local candidate believes more than half of the constituents in their district would favor them for political office. A random sample of 120 voters was polled, and 65 stated they would likely vote for the candidate. The P-value for the test of the hypotheses, and , is 0.18. What is the correct conclusion given

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

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, Ho: p=0.60 and Ha: p> 0.60, is 0.03. What is the correct conclusion given x=0.05?

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

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?

H0:p=.60,Ha:p>.60

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=.15,Ha:p=/.15

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?

Ho: p = 3; Ha: p< .3

A student believes that a certain 6-sided number cube, with the numbers 1 to 6, is unfair and is more likely to land with a 6 facing up. The student rolls the cube 100 times and lands with 6 facing up 20 times. Which hypotheses would test the student's claim?

Ho: p=.17 , Ha: p> .17

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?

NOT C: 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.

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

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, Ho: p=0.5 and Ha: p>0.5, is 0.2 , What is the correct interpretation of this value?

There is a 2% chance of getting a sample proportion of 0.64 or greater by chance alone if 0.5 is the true proportion.