Probability, Regression Analysis & Hypothesis Testing

1. (A) Classify the following as an example of nominal, ordinal, interval, or ratio level of measurement, and state why it represents this level: zip codes for the state of Pennsylvania
(B) Determine if this data is qualitative or quantitative: Nationality
(C) In your own line of work, give one example of a discrete and one example of a continuous random variable, and describe why each is continuous or discrete

2. A newsmagazine asks 1200 students what college they attend, and how many times per week they attend a party where alcohol is served. The news magazine determines the mean number of parties per week for each school, and publishes a ranking of the nation's top ten party schools.
I. What is the population?
II. What is the sample?
III. Is the study observational or experimental? Justify your answer.
IV. What are the variables?
V. For each of those variables, what level of measurement (nominal, ordinal, interval, or ratio) was used to obtain data from these variables?

3. 3. Construct both an ungrouped and a grouped frequency distribution for the data given below:
171 169 168 174 180 172 172 170 168 178
169 166 174 171 169 170 177 173 172 175

4. Given the following frequency distribution, find the mean, variance, and standard deviation. Please show all of your work.

Class Frequency
56-58 25
59-61 21
62-64 8
65-67 13
68-70 21

5. The following data lists the average monthly snowfall for January in 15 cities around the US:

8 35 31 26 36 41 29 40
17 16 33 38 30 34 13

Find the mean, variance, and standard deviation. Please show all of your work.

6. Rank the following data in increasing order and find the positions and values of both the 32nd percentile and 85th
percentile. Please show all of your work.
0 5 3 0 5 2 1 5 7 3 5 2

7. For the table that follows, answer the following questions:
x y
1 1/4
2 1/2
3 3/4
4

- Would the correlation between x and y in the table above be positive or negative?

- Find the missing value of y in the table.

- How would the values of this table be interpreted in terms of linear regression?

- If a "line of best fit" is placed among these points plotted on a coordinate system, would the slope of this line be positive or negative?

8. Determine whether each of the distributions given below represents a probability distribution. Justify your answer.

(A)
x 1 2 3 4
P(x) 11/25 6/25 3/25 1/5

(B)
x 3 6 8
P(x) 0.4 1/5 5/10

(C)
x 20 30 40 50
P(x) 0.41 0.07 0.32 0.2

9. A set of 50 data values has a mean of 15 and a variance of 36.
I. Find the standard score (z) for a data value = 30.
II. Find the probability of a data value > 30.
III. Find the probability of a data value < 30.
Show all work

10. Answer the following:
(A) Find the binomial probability P(x = 5), where n = 14 and p = 0.50.
(B) Set up, without solving, the binomial probability P(x is at most 5) using probability notation.
(C) How would you find the normal approximation to the binomial probability P(x = 5) in part A? Please show how you would calculate µ and &#963; in the formula for the normal approximation to the binomial, and show the final formula you would use without going through all the calculations

11. Assume that the population of heights of male college students is approximately normally distributed with mean &#61549; of 72.15 inches and standard deviation &#61555; of 6.39 inches. A random sample of 96 heights is obtained. Show all work.
(A) Find P(x > 73.25) _
(B) Find the mean and standard error of the X distribution _
(C) Find P(X > 73.25)
(D) Why is the formula required to solve (A) different than (C)?

12. Determine the critical region and critical values for z that would be used to test the null hypothesis at the given level of significance, as described in each of the following:

(A) Ho:&#956; = 86 and Ha:&#956; &#8800;86 &#61537; = 0.10
(B) Ho:&#956; &#8804;79 and Ha:&#956; <79 &#61537; = 0.05
(C) Ho:&#956; &#8805;70 and Ha:&#956; >70 &#61537; = 0.01

13. Describe what a type I and type II error would be for each of the following null hypotheses:

Ho: There is no good plan for the Iraq war

14. A researcher claims that the average age of people who buy theatre tickets is 49. A sample of 30 is selected and their ages are recorded as shown below. The standard deviation is 7. At &#61537; = 0.05 is there enough evidence to reject the researcher's claim? Show all work.

50 46 54 48 52 49 46 44 48 53
44 49 57 60 58 51 56 50 55 53
45 52 45 60 52 59 54 59 51 59

15. Write a correct null and alternative hypothesis for testing the claim that the mean life of a battery for a cell phone is at least 75 hours.