1.
a. Calculate μ and σ for the following set of scores and then convert each score to a z score: 64, 45, 58, 51, 53, 60, 52, 49.
b. Calculate the mean and standard deviation of these z scores. Did you obtain the values you expected? Explain.
2. Find the area of the normal distribution between the mean and z, when z equals
a. .18
b. .5
c. .88
d. 1.25
e. 2.11
3. Assume that the resting heart rate in humans is normally distributed with μ = 72 bpm (i.e.,beats per minute) and σ = 8 bpm.
a. What proportion of the population has resting heart rates above 82 bpm? Above 70 bpm?
b. What proportion of the population has resting heart rates below 75 bpm? Below 50 bpm?
c. What proportion of the population has resting heart rates between 80 and 85 bpm? Between 60 and 70 bpm? Between 55 and 75 bpm?
4.
a. If alpha were set to the unusual value of .08, what would be the magnitude of the critical z for a one-tailed test? What would be the values for a two-tailed test?
b. Find the one- and two-tailed critical z values for α = .03
c. Find one- and two-tailed z values for α = .007.
5. Assume that a large statistics class has just taken an exam with 300 multiple-choice questions. The distribution of grades was normal with a mean of 195 and a standard deviation of 30.
a. What two values of X (number of questions answered correctly) would encompass the middle 50% of the results?
b. 75% of the grades would be less than_____.
c. 95% of the grades would be between______and______.
6. Suppose that neighborhood soccer players are selling raffle tickets for $500 worth of groceries at a local store, and you bought a $1 ticket for yourself and one for your mother. The children eventually sold 1,000 tickets.
a. What is the probability that you will win?
b. What is the probability that your mother will win?
c. What is the probability that you or your mother will win?
7. Using the following table, please calculate the risk, risk ratio, odds, and odds ratio of receiving the death penalty if you are White vs. if you are non-White:
Defendant’s Race Yes No Total
White 20 130 150
Non-White 100 450 550
Total 120 580 700
8. In the last few years, an organization has conducted 200 clinical trials to test the effectiveness of anti-anxiety drugs. Suppose, however, that all of those drugs were obtained from the same fraudulent supplier, which was later revealed to have been sending only inert substances (e.g., distilled water, sugar pills) instead of real drugs. If alpha = .05 was used for all hypothesis tests, how many of these 200 experiments would you expect to yield significant results? How many Type I errors would you expect? How many Type II errors would you expect?
9. Using the data we collected, go to Analyze> Descriptive Statistics > Descriptives. Put in the Variables box “fb”. Click on the box that says “Save standardized values as variables.” This will give you all the z-scores. In the options box, click on mean and standard deviation. Click continue, then Paste and Run. The output should be a box with the means and standard deviations, and the Data will have a new column labeled Zfb. These are your z-scores.
10. Assume that number of facebook friends is normally distributed. Using the z-scores you calculated using SPSS and the table of probabilities for the standard normal distribution (Table E.10), answer the following questions:
a. What proportion of participants has more facebook friends than Subject #160?
b. What proportion of the participants have less facebook friends than Subject #118?
c. What proportion of the participants have between Subjects #2 and #3’s amount of facebook friends?
d. What number of facebook friends would put you in the top 10%?
e. What number of facebook friends would put you in the bottom 5% (of those who use facebook)?
11. We are interested in whether our friends and family have more facebook friends than does the general population of Americans, which is known to be 120.
a. What is the null hypothesis (words and symbols)?
b. What is the alternative hypothesis (words and symbols)?
c. Using SPSS, show graphically the distribution of facebook friends from your sample. Describe this distribution.
d. What is the mean number of facebook friends (use SPSS)?
e. What is the standard deviation (use SPSS)?
f. What is the standard error?
g. Pretend instead that the mean and standard deviation you obtained had come from a sample of 100 of our friends and family. What would happen to the standard error? What if the sample came from 10 of our friends and family?
h. Would you use a one- or two-tailed test to test your hypothesis? Provide an argument in favor of both options.