LAB ACTIVITY 10

Due Friday, Oct. 28 at 11:59pm

(Use ‘UCDavis2.mtw’ dataset)

Activity 1 (Requires Minitab): How does the p-value change as the sample size or p-hat changes?

For the problems below we are testing H0: p=.5 vs. Ha p>.5.

  1. First we investigate how the p-value changes when the sample proportion remains constant but the sample size changes. For each entry in the table below, fill in the missing values. For the p-values you will need to use the Minitab sequence Stat  Basic statistics 1 proportion  choose ‘summarized data’ from drop-down menu  enter the desired X as number of events and n as number of trials  make sure ‘perform hypothesis test’ is checked and that you use the options button to set the alternative as “>” and to use the normal approximation  OK

Sample size / Sample proportion / X / p-value
50 / 0.60
100 / 0.60
500 / 0.60
  1. Next we investigate how the p-value changes when the sample proportion changes but the sample size remains the same. For each entry in the table below, fill in the missing values.

Sample size / Sample proportion / X / p-value
50 / 30
50 / 33
50 / 35
  1. Based on the tables above choose the correct answers:
  1. If the sample proportion stays the same but the sample size increases, the p-value will….

increasedecreaseremain the same

  1. If the sample proportion increases (and our alternative is “”), while the sample size stays the same, the p-value will….

increasedecreaseremain the same

Activity 2 (Requires Minitab): Hypothesis testing for a population proportion.

Open the dataset UCDavis2 (available on Angel). This is a random sample of students from the University of California at Davis. The variable ‘Friends’ is a response to the question “With whom do you find it easiest to make friends, people of the same sex or opposite sex?(circle one)”

  1. We want to answer the question “Do more than 50% of UC Davis students find it easier to make friends with people of the opposite sex?”

Let p= the population proportion of people who make friends easier with people of the opposite sex. In terms of p, write the correct null and alternative hypotheses.

H0: ______

Ha: ______

  1. Use Minitab to calculate p-hat. (You may want to refer to Lab #9, Activity 2, question 1 for the Minitab commands that will give you a table of counts that can serve as the basis for this calculation.)
  1. If the null hypothesis is true, what are the mean and standard deviation of the sampling distribution of p-hat? (This answer will have nothing to do with your answer to the previous question 2.)
  1. Mean =
  2. Standard deviation =
  1. Calculate the z-statistic for this hypothesis test. (This answer, which tells how many standard deviations p-hat is from the mean if we assume H0 to be true, combines your answers to questions 2 and 3.)
  1. a. Use Minitab to calculate the p-value. (Use your answer from question 4, together with the direction of the alternative hypothesis, then find the correct standard normal probability using Graph  Probability Distribution Plot etc.)
  1. What is the correct interpretation of this p-value?
  1. What is the conclusion based on the p-value? Be sure to state something specific about the research question.You may use a cutoff of 0.05 to determine statistical significance.

Activity 3 (Does not require Minitab). Writing the correct null and alternative hypotheses.

For each of the following situations, write the correct null and alternative hypotheses in terms of the population proportion p. Further indicate whether each alternative is one-sided or two-sided. In answering, keep in mind that sample data are irrelevant when constructing hypotheses.

  1. Bill, a psychologist, has developed a new aptitude test. He was able to show (through a somewhat dubious study) that 80% of the public passed the test. A second psychologist, Tamera, wants to recreate this study. She believes the actual percentage is less than 80%. A random sample of 200 people took the test, and 146 passed. What null and alternative hypotheses should Tamera test?

H0: ______

Ha: ______

one-sided two-sided

  1. A card company claims that 80% of all American college students send a card to their mother on Mother's Day. Suppose you plan to gather your own data to test this claim. You aren’t sure if the true proportion should be larger or smaller than the claim. You select a simple random sample of 400 American college students to determine the proportion of them who send a card to their mother on Mother's Day. Your sample indicates that 70% of the students sampled send a card to their mother on Mother's Day. What null and alternative hypotheses should you test?

H0: ______

Ha: ______

one-sided two-sided

  1. A student wanted to study the ages of couples applying for marriage licenses in his county. He studied a sample of 94 marriage licenses and found that in 67 cases the husband was older than the wife. Do the sample data provide evidence that the husband is usually older than the wife among couples applying for marriage licenses in that county? What null and alternative hypotheses should you test?

H0: ______

Ha: ______

one-sided two-sided

  1. The experience of unrequited love is virtually universal at some point in life. It is believed that only 5% of adults have never experienced it. Some social psychologists think the percentage is even lower. What null and alternative hypotheses should they test to prove their claim?

H0: ______

Ha: ______

one-sided two-sided