Introduction to Hypothesis Testing Answers

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 ?

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?

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?

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 ?

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?

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?

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?

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, and , is 0.24. What is the correct conclusion given ?

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 24 chips are defective. Which hypotheses would test if the proportion of defective chips is more than 10%?

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?