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MATH 136
FINAL REVIEW
1. In an experiment testing a herbal extract of echinacea versus vitamin C against the common cold 60
college students in good health are randomly selected to participate. Design an experiment. Include a
control group. Carry out the randomization beginning at Row 04 Column 06 in Table I Random Digits.
2. On the first day of class one semester, 30 students were asked for their one-way travel times from
home to college(to the nearest five minutes). The resulting data were as follows:
20 20 30 25 20 25 35 25 15 25
25 40 25 30 15 20 45 25 15 20
20 20 20 25 5 20 20 10 5 20
a) Make a stemplot.
d) Give the 5# summary
b) Identify your fences.
e) Draw the boxplot.
c) Are there any outliers?
f) Shape.
3. The speeds of 55 cars were measured by a radar device on a city street:
27 23 22 38 43 24 35 26 28 18 20
25 23 22 52 31 30 41 45 29 27 43
29 28 27 25 29 28 24 37 28 29 18
26 33 25 27 25 34 32 36 22 32 33
21 23 24 18 48 23 16 38 26 21 23
a) Make a histogram with 8 classes.
b) Identify your classes in a frequency table.
c) Comment on the distribution.
4. The following data are the ages and the asking prices for 19 used foreign compact cars:
Age(years)
3 5 3 6 4 4 6 7 2 2 6 8 5 6 5 7 4 7 5
Price(x$100) 68 52 63 24 60 60 28 36 68 64 42 22 50 36 46 36 48 20 36
a) Draw a scatter plot
b) Calculate the equation of the line of best fit.
c) Graph the regression line on the scatter plot. Show the points used.
d) What is the correlation?
e) What percent of variation between x and y can be explained by a linear model?
f) Predict the average asking price for all foreign cars that are five years old.
5. Did you ever wonder “How many times buyers see an infomercial before they purchase its product or
service?” The USA Snapshot “Television’s hard sell”(10-21-94) answers that question. According to the
National Infomercial marketing Association:
Times Watched Before Buying
1
2
3
4
5 or more
Proportion of Buyers
.27 .31 .18 .09 .15
a) Is this a probability distribution? Justify your answer.
b) What is the probability that a buyer watched only once before buying?
c) What is the probability of buyers that watched the infomercial three or more times before
purchasing?
d) Compute the mean and standard deviation.
6. The heights of kindergarten children are approximately normally distributed with ? = 39 and o = 2.
a) If an individual kindergarten child is selected at random, what is the probability that he or she has a
height of more than 40 inches? Include a sketch.
b) If an individual kindergarten child is selected at random, what is the probability that he or she has a
height between 38 and 40 inches? Include a sketch.
c) A classroom of 30 of these children is used as a sample. What is the probability that their mean
height is more than 40 inches? Include a sketch.
d) A classroom of 30 of these children is used as a sample. What is the probability that the class mean
will be between 38 and 40 inches? Include a sketch.
7. IQ scores are normally distributed with a mean 100 and standard deviation 15.
a) What percent of the population has an IQ below 90? Include a sketch.
b) What percent of the population has an IQ between 90 and 120? Include a sketch.
c) What score separates the top 5%? Include a sketch.
8. A bowl contains 4 Blue and 3 Green balls. Two balls are selected at random without replacement.
a) Make a tree diagram showing all possible outcomes with their probabilities.
b) P(GG)
c) P(exactly one Blue)
d) P(at least one Blue)
9. A baseball player has a 0.300 batting average. In one game the player has 4 at bats.
a) What is the probability that they will get exactly 2 hits?
b) What is the probability that they will get exactly 2 or more hits?
c) Make a table of probabilities for the possible outcomes.
d) Make a probability histogram and describe the shape.
10. Make a sketch, compute the p-value and state your conclusion about Ho.
a) Ha p 0 n = 16 t = 1.516
d) Ha ?1 – ?2 ? 0 n1 = 16, n2 = 22 t= 2.135
11. Heights in Inches from a past class:
Males
63 72 73 66 71 69 72 75 70 71 70
Females 67 65 62 63 64 68 67 64 66 65 66 67 67
a) Construct a 90% Confidence Interval for the difference of the mean heights of males and females.
Include, the sample statistics, degrees of freedom, ?? , standard error and a sentence.
2
b) Test the claim: mean heights of males are greater than females. State the hypotheses, standardize
and give degrees of freedom. Include a sketch, state the p-value followed by your conclusion.
12. Most pregnancies result in live births, but some end in miscarriages or stillbirths. A June 2001
National Vital Statistics Report examined those outcomes in the United States during 1997, broken
down by the age of the mother. The table shows counts consistent with that report. Is there evidence
that the distribution of outcomes is not the same for these age groups? Perform a chi-square test.
Age of Mother
Live Births
Fetal Losses
Under 20
49
13
20-29
201
41
30-34
88
21
35 or over
49
21
a) What kind of chi-square test is appropriate; goodness-of-fit, homogeneity or independence?
b) State the Hypotheses. c) Compute the expected cell values. d) Calculate the test statistic ? 2 .
e) Make a sketch, give the degrees of freedom.
f) Find the p-value and state your conclusion followed by a summary sentence.
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