QS381 FINAL EXAM

QS381 FINAL EXAM Winter 2001 Gordie Swartzman – Instructor

Sarah Butler – Teaching Assistant

March 14 2001

Name: __________________________________________________

Please answer all questions and show all work.

1. (15 pts)The table below shows the numbers of voters in the US by age based on a recent census.

Age of Voters Frequency (millions)
18-20	10.8
21-24	13.9
25-34	40.1
35-44	43.3
45-64	53.7
65-84	31.9

a) (3)Find the probability that a voter chosen at random is between 21 and 24 years of age.

b) (3) Find the probability that a voter chosen at random is between 35 and 64 years of age.

c) (3) Find the probability that a voter chosen at random is less than 65 years of age.

d) (6) Find the mean age of this voting population.

Name: __________________________________________________

2. (20 pts) For each of the terms in the left column is the definition on the left correct. If not suggest a suitable correction.

a The probability of accepting a true null hypothesis

c² A symmetric probability distribution used to test for differences between means for small samples

s The population variance

N(0,1) The standard normal distribution

r²the correlation coefficient between two sampled variables

Binomial distribution A probability distribution for the number of successes in n independent trials

Central limit theorem A theorem that says that 95% of all observations lie within 2 standard deviations of the mean.

Box and whisker diagram A diagram showing the median, quartiles, range and mean of a sample

Confidence interval The range of values around the population mean (or any population parameter) that is expected to contain the sample mean with some pre-chosen probability.

t_cThe cutoff for the rejection region in a normal probability distribution

Name: __________________________________________________

3.(30 pts)The table below shows reading test scores for two groups of third graders. The first group of 21 students participated in directed reading activities for 10 weeks (column 1). The second group of 23 students followed the same curriculum without directed reading activities (column 2). Both classes took the same reading test after their curriculum.

Reading scores test
24	42
43	43
58	55
71	26
43	62
49	37
61	33
44	41
67	19
49	54
53	20
56	85
59	46
52	10
62	17
54	60
57	53
33	42
46	55
43	28
57	48
	37
	42
51.47619	41.52174
Mean x1	Mean x2
121.1619	294.0791
s₁²	s₂²

a. (10) Draw a stem and leaf diagram for each population. Do the populations appear to be normally distributed?

b. (10) Assuming the populations are normally distributed, test for equality of variance between the two populations for significance level a=0.10.

c. (10) Given the populations are normally distributed test the claim that the performance of the third grade students with the directed reading activities (population 1 above) performed better on the test than those without the activities at significance level a=0.05. Interpret the results of the test.

Name: __________________________________________________

4. (15 pts.) 52% of adults say chocolate chip is their favorite cookie. A community bake sale has prepared 350 chocolate chip cookies. The bake sale attracts 650 adult customers (what no kids?) and each buys one cookie (their favorite). What is the probability there will not be enough chocolate chip cookies?

5. (20 pts.) The following table gives the median age in years of cars and trucks on the road in the US for seven different years.

Median age of vehicles on road
Cars, x	Trucks, y
8.1	7.8
7.7	7.6
6.5	6.5
6.9	7.6
6	6.3
5.4	5.8
4.9	5.9

a. (5) Draw a scatterplot for these data. Label both axes. What kind of relationship is there between the median age of cars and trucks?

b. (5) Compute the correlation coefficient between the median age of cars and trucks on the road.

c. (5) Test the null hypothesis that the population correlation coefficient r=0 with a=0.05.

d. (5) Find the coefficient of determination of these data.