Statistics Problem Set #2

For all of these, you must show your work and all the steps you took. Use a spreadsheet to show your work. Each question also requires a full typed answer (using complete sentences, etc.), and do this for each of the a), b), c) etc. when there are sub-questions.

The value for each answer is indicated. Maximum total points = 66

Correlation and Prediction

1. Using Excel (or your program of choice), create scatterplots (aka scattergram or scatter diagram) using 12 points showing: a) a perfect positive linear correlation, b) a strong but not perfect linear positive correlation, c) a plot that shows no linear correlation, and d) a weak negative linear correlation. (4 points)

2. Gable and Lutz (2000) studied 65 children, 3 to 10 years old, and their parents. One of their results was: “Parental control of child eating showed a negative association with children’s participation in extracurricular activities (r = -.34, p < .01)” (p. 296). Another result was: “Parents who held less appropriate beliefs about children’s nutrition reported that their children watched more hours of television per day (r = .36, p < .01)” (p. 296).

Explain these results to someone who never had a course in statistics. Be sure to describe the observed correlations, what they might mean and any possible direction of causality. That means you identify potential predictor variables! (6 points)

Making Inferences from Statistics - Normal Distribution and Probability

3. Suppose the people living in a city have a mean score of 40 and a standard deviation of 5 on a survey about concern about the environment. Assume scores on this survey are normally distributed.

i - Approximately what percentage of people in this city have a score a) above 40, b) above 45, c) above 30, d) below 35. Explain how you get your answer without using a normal curve table. (5 points)

ii - What is the minimum score a person has to have to be in the top a) 2%, b) 16%, c) 50%, d) 98% of respondents. (4 points)

4. Assuming a normal distribution of scores, a) if a student is in the bottom 30% of the class on Spanish ability, what is the highest Z score this person could have? b) what is the lowest score a student in the top 10% could have? (4 points)

5. You apply to 20 graduate programs, 10 of which are in the USA, 5 of which are in Canada, and 5 of which are in Australia. You get a text from your roommate that you have a letter from one of the programs you applied to, but nothing is said about which one (thanks roomy!). Give the

probability it is from a) one in the US, b) one in Canada, c) one that is not in Australia. Show how you worked out your responses. (3 points)

6. Suppose you plan to conduct a survey of visitors to the campus. You want the survey to be as representative as possible. How would you select people to survey? And explain why you believe that to be the best method. (4 points)

Hypothesis Testing

7. When a result is not extreme enough to reject the null hypothesis, explain why it is wrong to conclude that your result supports the null hypothesis. (3 points)

8. For each of the following, state: a) what two populations are being compared; b) the research hypothesis, c) the null hypothesis; d) the independent variable; e) the dependent variable; and f), whether it is a one-tailed (directional) or two-tailed test (non-directional), and explain your rationale.

i) In an experiment, people are told to solve a problem by focusing on the details. Is the speed of solving the problem different for people who get those instructions compared to people who get no special instructions? (4 points)

ii) Based on reports in which the status of women is scored on a 10-point scale, the mean and standard deviation across many cultures are known. A new culture is found wherein there is an unusual family arrangement. Do cultures with the unusual family arrangement provide higher status to women than cultures in general? (4 points)

iii) Do people who live in big cities develop more stress-related conditions than people in general? (4 points)

9. A researcher predicts that listening to music while solving math problems will make a particular brain area more active. To test this, a research participant has her brain scanned while listening to music and solving math problems. The brain area of interest shows a 5.8% signal change. From many previous studies with this same math problem procedure (but without listening to music) it is known that the signal change in this brain area is normally distributed with a mean of 4.5 and a standard deviation of 1.0. Using the .01 level what should the researcher conclude? Describe how you solve the problem using all five steps of hypothesis testing. (6 points)

10. Why is the standard deviation of the distribution of means smaller than the standard deviation of the distribution of the population of individuals? Explain fully! (3 points)

11. Under what conditions is it reasonable to assume that a distribution of means will follow a normal curve? (2 points)

12. Twenty-five women between the ages of 70 and 80 were randomly selected from the general population of women their age to take part in a special program to decrease reaction time (increase response speed). After the course, the women had an average reaction time of 1.5 seconds. Assume that the mean reaction time for women of this age range is 1.8 s, with a standard deviation of 0.5 s. What should you conclude about the effectiveness of the course?

a) using the .01 level of significance carry out the steps of hypothesis testing and show your work.

b) determinethe99%confidenceinterval.

c) what can you conclude about the special program and the mean of a population of

women given the special program? Explain.

(10 points)