Find the mean and standard error of the x distribution and

Question

1. (A) Classify the following as an example of nominal, ordinal, interval, or ratio level of measurement, and state why it represents this level: temperature in 25 US cities

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

(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. An insecticide company exposes 10,000 cockroaches to its newest product, and exposes another 10,000 to their previous formula.  The researchers use videotape to count how many cockroaches are still alive, and how many appear to be in distress, at 10 second intervals.  When the test is completed, the researchers determine the mean elapsed time before a cockroach was killed by each product.

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? (Points : 12) 3. Construct both an ungrouped and a grouped frequency distribution for the data given below:

207   211   204   208   202   203   211   202   205   212
210   212   204   199   204   201   213   200   204   207

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

Class	Frequency
71-73	17
74-76	8
77-79	12
80-82	7
83-85	16

5. The following data lists the average monthly snowfall for January in 15 cities around the US:
 
21    5     43    39    45    42    26    40
38    32    17    23    31    28    16
 
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 16^th percentile and 91^st percentile.  Please show all of your work.

4   5   4   9   9   1   0   7   4   8   0   9

x	y
1	-1/3
2	-2/3
3	-1
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)	3/5	12/25	3/25	0

(B)

x	3	6	8
P(x)	0.15	3/5	0.25

(C)

x	20	35	40	50
P(x)	0.45	0.25	1/4	0.05

9. A set of 50 data values has a mean of 28 and a variance of 4.

I.  Find the standard score (z) for a data value = 31.

II. Find the probability of a data value > 31.

III. Find the probability of a data value < 31.

Show all work.

 10. Answer the following:

(A) Find the binomial probability P(x = 5), where n = 12 and p = 0.70.

(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. (Points : 9)

11. Assume that the population of heights of male college students is approximately normally distributed with mean m of 69.34 inches and standard deviation s of 3.58 inches. A random sample of 76 heights is obtained.  Show all work.

(A)  Find P(x>69.25)

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

(C)  Find p(x>69.25)

(D)  Why is the formula required to solve (A) different than (C)?

13. Describe what a type I and type II error would be for each of the following null hypotheses: H0: There is no nuclear waste in the US.

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 a = 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