Download Part 1 - Hope College Math Department

Chapters 6-8 Review
Part 1
1. Circle the correct answer (increases or decreases) for each of the following
statements about power.
a) As the population correlation moves farther from 0, power: increases decreases.
b) As the sample size increases, power: increases decreases.
c) As the significance level decreases, power: increases decreases.
d) As the population means get closer together, power: increases decreases.
e) As the population standard deviations increase, power: increases decreases.
2. Suppose you have the following situations where you are going to use the power
calculator to determine the sample size needed to achieve 80% power at the 5%
significance level. Circle the value that will be the most conservative one to use (i.e.
the one the will give you the largest sample size with the power calculator)
a) Testing correlation: Do you use a correlation of 0.2 or 0.4?
b) Testing means: Do you use a difference in means of 1 or 2?
c) Testing means: Do you use a standard deviations of 2 or 3?
3. Multiple Choice. Power is defined to be:
a)
b)
c)
d)
The probability of concluding the alternative hypothesis if it is actually true.
The probability of concluding the null hypothesis if it is actually true.
The probability of concluding the alternative hypothesis if it is actually false.
The probability of concluding the null hypothesis if it is actually false.
4. Multiple Choice. Which distribution below has the smallest standard deviation?
a) A
b) B
c) C
d) All three distributions have the same standard deviation.
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Chapters 6-8 Review
210 class survey
5. Multiple Choice. The heights of 256
statistics students ranged from 59 to 78
inches. The mean was about 67.7 inches
and the distribution is shown at the right.
What is the best estimate for the standard
deviation?
a)
b)
c)
d)
−3.2
4
10
20
Histogram
50
40
30
20
10
58 60 62 64 66 68 70 72 74 76 78 80
height
6. Multiple Choice. Which of the following is a condition that should be met in order to
run a traditional independent samples t-test?
a)
b)
c)
d)
The standard deviations for each group should be the same.
The sample sizes for each group should be the same.
The difference in means should be positive.
If your sample size is small, the sample data for each group should not be
strongly skewed or contain outliers.
7. Multiple Choice. Suppose you are conducting a test of significance for the weight of
Snickers bars. Your null hypothesis is H0: The population mean weight is 16.4
grams and your alternative hypothesis is Ha: The population mean weight is more
than 16.4 grams. From your random sample of 40 Snickers bars, you conclude that
the mean weight of all Snickers bars is more than 16.4 grams with a p-value of 0.02.
Which of the following statements best describes what that p-value means?
a) If the mean weight of all Snickers bars is 16.4 grams, the probability that a
random sample of 40 Snickers would have a mean as high or higher than the
one we found is 0.02.
b) If the mean weight of all Snickers bars is more than 16.4 grams, the probability
that a random sample of 40 Snickers would have a mean as high or higher than
the one we found is 0.02.
c) The proportion of Snickers bars that have weights more than 16.4 grams is 0.02.
d) The probability that the mean weight of all Snickers bars is more than 16.4 grams
is 0.02.
8. Multiple Choice. A confidence interval will increase in width if:
a)
b)
c)
d)
Either the sample size increases or the confidence level increases.
Either the sample size increases or the confidence level decreases.
Either the sample size decreases or the confidence level increases.
Either the sample size decreases or the confidence level decreases.
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Chapters 6-8 Review
9. Multiple Choice. You have taken a random sample of 30 grade point averages from
Hope College students. You determine that a 95% confidence interval for the mean
grade point average is 2.9 to 3.3. Which of the following statements gives a valid
interpretation of this interval?
a) 95% of the 30 grade point averages in the sample are between 2.9 and 3.3.
b) 95% of all Hope College students have grade point averages that are between
2.9 and 3.3.
c) If the procedure were repeated many times, 95% of the sample means would be
between 2.9 and 3.3.
d) If the procedure were repeated many times, 95% of the time the resulting interval
would contain the mean grade point average of all Hope College students.
10. Multiple Choice. The width of a confidence interval for the estimate of a population
proportion will be
a) Wider when the sample proportion is 0.95 than when the sample proportion is
0.55.
b) Wider for 90% confidence than for 95% confidence.
c) Narrower for a sample size of 50 than for a sample size of 100.
d) Narrower when the sample porportion is 0.10 than when the sample proportion is
0.45.
11. Multiple Choice. Which of the following is an example of a matched pairs design
(dependent samples)?
a) A teacher compares the pre-test and post-test scores of a group of students.
b) A teacher compares the scores of students using a computer based method of
instruction with the scores of other students using a traditional method of
instruction.
c) A teacher compares the scores of students in her class on a standardized test
with the national average score.
d) A teacher calculates the average of scores of students on a pair of tests and
wishes to see if this average is larger than 80%.
12. Multiple Choice. You run a hypothesis test for H0: There is no difference between
the means, and Ha: There is a difference between the means. You obtain a P-value
of 0.022. Which of the following statements must be true?
a)
b)
c)
d)
A 95% confidence interval for µ will include the value 1.
A 95% confidence interval for µ will include the value 0.
A 99% confidence interval for µ will include the value 1.
A 99% confidence interval for µ will include the value 0.
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Chapters 6-8 Review
13. Suppose test scores form a bell-shaped (normal) curve with a mean of 50 and a
standard deviation of 5.
a) Give the interval in which the middle 95% of all scores lie.
b) What percent of scores will be above 55?
14. How much do bags of carrots that are labeled one pound actually weigh? A student
researcher weighed “one pound” bags of carrots. Use the Fathom worksheet
carrot_weights.ftm to find a 95% confidence interval for the population mean weight
of all “one pound” bags of carrots. (These are labeled as the small_bags in the
worksheet.) Assume the data came from a random sample and is accurate.
15. Do a majority of all female Hope freshmen have at least one credit card? To answer
this question, some student researchers collected data from 42 female Hope
freshmen. They found that 27 of them had at least one credit card. Assume the
statistics came from a random sample and are accurate. Use Fathom to test at the
5% significance level to determine if a majority of all female Hope freshmen have at
least one credit card. Write out the null and alternative hypotheses, the p-value, and
your conclusion.
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Chapters 6-8 Review
Part 2
Data Set.
Name: Automobiles (on Moodle in Fathom and PASW)
Abstract: This is a study of 1996 automobiles.
Variables (column):
1. Model
2. Type of Drive (0=Rear, 1=Front)
3. MPG (Mileage per gallon)
4. Fuel type (0=Premium, 1=Regular)
5. Fuel capacity (in gallons)
6. Length (in inches)
7. Wheelbase (in inches)
8. Width (in inches)
9. Turning circle (in feet)
10. Weight (in pounds)
11. Luggage Capacity (in cubic feet)
12. Front Leg Room (in inches)
13. Front Head Room (in inches)
For each question answer the following. (Use Fathom as necessary or to check that
you are looking at the right thing in the PASW output.) Note that most problems require
either a test or an interval, but we are doing both for completeness.
a. Is it an A, B, C, or E problem?
b. Give appropriate descriptive statistics and graph.
c. Run test.
d. Sketch the shape of the sampling distribution if the null hypothesis is true, and
indicate where the measure of the data falls.
e. Get and interpret confidence interval.
f. Do you think the assumptions are met to run a traditional analysis?
1. Are more than half of the cars front wheel drive? Also, estimate what the proportion
of front wheel cars.
2. Is the average MPG different than 25 MPG? Also, estimate what the average MPG
is.
3. Do rear wheel drive cars tend to get less average MPG than front wheel drive cars?
Also, estimate what the difference is.
4. Do cars that weigh more tend to get less average MPG? Estimate how much MPG
goes down when weight goes up by a pound.
5. Give another question you could explore from this data set for each type of Analysis
A, B, C, and D. Perform each analysis.
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Chapters 6-8 Review
Part 3
Name: Tulip Time 5K Run
Abstract: This data is a sample including observations of 297 participants running the Tulip Time
5K in 2007. Observations included three different variables.
Variables (column):
1. Time (mm:ss)
2. Age (Years)
3. Gender (0=Female, 1=Male)
Review Questions. For each question answer the following.
g. Is it an A, B, C, or E problem?
h. Give appropriate descriptive statistics and graph.
i. Run test.
j. Sketch the shape of the sampling distribution if the null hypothesis is true, and
indicate where the measure of the data falls.
k. Get and interpret confidence interval.
l. Do you think the assumptions are met to run a traditional analysis?
1. Is the average time to complete a 5K race significantly different than 30 minutes?
Give a 95% confidence interval for average time.
2. Is the average age of participants significantly different than 35? Give a 95%
confidence interval for average age.
3. Is there significant evidence that a majority of race participants are male? Estimate
the true proportion of males in 5K races with 95% confidence.
4. As people age, do their race times tend to be longer? Estimate (with 95%
confidence) how many minutes are added to race times for each additional year of
age.
5. Do females on average have longer race times than males? Estimate (with 95%
confidence) how much slower females are than males on average.
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