1.5.5) Suppose a friend of yours says she is a 75% free-throw shooter in basketball. You don't think she is that good and want to test her to gather evidence that she makes less than 75% of her free throws in the long run. You have her shoot 30 free throws, and she makes 18 (or 60%) of them. Are the validity conditions met for the one-proportion z-test?

A. No, because the sample size is less than 40.

B. No because the number of success and failures are each at least 10.

C. Yes because the sample size is more than 20.

D. Yes because the number of success and failures are each at least 10.

1.5.30 Statistics students were asked to randomly pick a whole number between 1 and 10. Sixty-two out of 101 students picked a number greater than 5. If they truly randomly picked their numbers, we would expect about half the students would pick a number greater than 5 in the long run. Do statistics students randomly choose a number or not? Test by answering (a)-(e).

a. Stating the hypotheses in words and in symbols.

b. Give the value of the statistic.

c. Are the validity conditions met? Explain.

d. Use the One Proportion applet to give both a simulation-based and theory-based p-value.

e. Write out a conclusion in the context of the research question.

1.5.33 Whereas flipping a coin should result in 50% heads and 50% tails in the long run, will spinning coins on a table give the same result or not? Test this with a coin of your choice, making sure you have enough trials to meet the validity conditions of a one-proportion z-test by doing (a)-(e).

a. State the hypotheses in words and in symbols.

b. Give the sample statistic symbol and the value you obtain.

c. Calculate the theoretical standardized statistic.

d. Use the One Proportion applet to give both a simulation-based and theory-based p-value.

e. Write out a conclusion in the context of the research question.

Argue whether or not you believe using a sample of students from your school's cafeteria (you recruit the next 100 people to visit the cafeteria to participate) may or may not yield biased estimates based on the variable being measured/research question being investigated in each of situations in (a)-(d).

a. Using the proportion of students with Type O blood to learn about the proportion of U.S. adults with Type O blood

b. Using the proportion of students who eat fast food regularly to learn about the proportion of U.S. college students who eat fast food regularly

c. Using the proportion of students who have brown hair to learn about the proportion of all students at your school who have brown hair

d. Using the proportion of students who have brown hair to learn about the proportion of all U.S. adults who have brown hair.