I NEED THESE 4/28/12 by 3p central time. I have no idea how to work these out. Please help!!!! ASAP!

1. (A) Classify the following as an example of nominal, ordinal, interval, or ratio level of measurement, and state why it represents this level: eye color

 (B) Determine if this data is qualitative or quantitative:  weight

 (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 group of 200 adults aged 21 to 50 were selected from those entering Fit Right Health stores in Washington State, and were randomly divided into two groups.  One group was given an herb and the other a placebo.  After 6 months, the number of respiratory tract infections in each group were compared.

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. Construct both an ungrouped and a grouped frequency distribution for the data given below:

42   46   52   50   54   51   51   49   54   42  

55   49   53   50   55   41   53   52   47   45

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

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

 34    9     28    24    0     46     34    20

 1     38    5      16    32    26    25

 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 11th percentile and 71^st percentile.  Please show all of your work.

7   5   3   2   9   6   4   3   8   5   5   8  

7. For the table that follows, answer the following questions:

-  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)

(B)

(C)

9. A set of 50 data values has a mean of 18 and a variance of 4.  Show all work.

  I.  Find the standard score (z) for a data value = 20.

 II. Find the probability of a data value < 20.

 III. Find the probability of a data value > 20.

10. Answer the following:

(A) Find the binomial probability P(x = 5), where n = 15 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 σ 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 µ of 73.16 inches and standard deviation σ of 6.39 inches. A random sample of 70 heights is obtained.  Show all work. 

(A)  Find   P(x > 74.50)

 (B)  Find the mean and standard error of the  x̄  distribution

 (C)  Find   P(x̄ > 74.50)

 (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) H_o: µ ≥ 53  and  H_a: µ < 53,   a = 0.01

(B) H_o: µ ≤  and  H_a: µ > 32,   a = 0.05

(C) H_o: µ = and  H_a: µ ≠ 24,   a = 0.10

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

H_o:  There is no difference in treatment methods.

14. A researcher claims that the average age of people who buy lottery tickets is 61. A sample of 30 is selected and their ages are recorded as shown below. The standard deviation is 8.  At α = 0.01 is there enough evidence to reject the researcher’s claim?  Show all work.

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 85 hours.