Question/Answers:
You should work each of the following on your own, then review the solution’s guide. DO NOT look at the solution’s guide first.
1. The following numbers
represent the weights in pounds of six 7year old children in Mrs. Jones'
second grade class (25, 60, 51, 47, 49, 45). Find the mean, median, mode,
variance, and standard deviation.
2. If the variance is 846,
what is the standard deviation?
3. If we have the following
data: 34, 38, 22, 21, 29, 37, 40, 41, 22, 20, 49, 47, 20, 31, 34, 66. Draw a
stem and leaf. Discuss the shape of the distribution.
4. For two events, C and D,
P(C) = 0.6, P(D)=0.3, and P(CD) = 0.2. Find P(CÇD).
5. If a binomial variable has
n=34 and p=0.30, find the mean, variance, and standard deviation.
6. A company claims that 61%
of consumers know about their product.
If the company asks 18 consumers, what is the probability that (a)
exactly 10 will say yes, that (b) between 10 and 12 will say yes.
7. If the population has a
mean of 58 and a standard deviation of 23.4, what would be the mean and
standard deviation of a sampling distribution with a sample size of 22?
8. A restaurant asks 40 customers
about their service times. If the population mean service time is 28 minutes
with a standard deviation of 5.1 minutes, what is the probability that the mean
of the sample service times would be less than 26 minutes?
9. On a dry surface, the
braking distance (in meters) of a certain car is a normal distribution with mu
= μ = 45.1 m and sigma = σ = 0.5.
a. Find the braking distance that represents the 91st percentile.
b. Find the probability that the braking distance is less than or equal
to 45 m.
c. Find the probability that the braking distance is greater than 46.8
m.
d. Find the probability that the braking distance is between 45 m and
46.8 m.
10. A sample of 58 days of gas
prices has a mean of $2.75 and a standard deviation of $0.86. Construct the 95%
confidence interval.
11. A drug manufacturer wants
to estimate the mean heart rate for patients with a certain heart condition. Because
the condition is rare, the manufacturer can only find 14 people with the
condition currently untreated. From this small sample, the mean heart rate is
101 beats per minute with a standard deviation of 8.
a. Find a 99% confidence interval for the true mean heart rate of all people
with this untreated condition. Show your calculations.
b. Interpret this confidence interval, and write a sentence that explains
it.
12. Determine the minimum
required sample size if you want to be 80% confident that the sample mean is
within 2 units of the population mean given sigma = 9.4. Assume the population
is normally distributed.
13. A social service worker
wants to estimate the true proportion of pregnant teenagers who miss at least
one day of school per week on average. The social worker wants to be within 5%
of the true proportion when using a 90% confidence interval. A previous study estimated
the population proportion at 0.21.
a. Using this previous study as an estimate for p, what sample size should
be used?
b. If the previous study was not available, what estimate for p should
be used?
14. A restaurant claims that
its speed of service time is less than 15 minutes. A random selection of 49
service times was collected, and their mean was calculated to be 14.5 minutes.
Their standard deviation is 2.7 minutes. Is there enough evidence to support
the claim at alpha = .07? Write the hypotheses, the pvalue, conclusion, and
implication for the claim.
15. To support their claim that
the average speed on their road is more than 25 mph, neighbors collect data on
24 cars on a day. Those cars have a mean speed of 26.7mph and a standard
deviation of 3.9mph. Do the neighbors
have enough information to support their claim at an alpha of 0.05? Write the
hypotheses, the pvalue, conclusion, and implication for the claim.
16. A doctor claims that 30% of
patients only have a cold. During one month, the doctor finds that 112 of 420
patients only has a cold. At α=0.06, can the doctor support the claim? Write
the hypotheses, the pvalue, conclusion, and implication for the claim.
17. To test if there was a
positive relationship between the dependent and independent variables, a
hypothesis test found a tstatistic of 1.43 based on a sample size of 20. Based
on this information, what could be concluded about the relationship between
these variables using an alpha of 0.05?
18. In a multiple regression with
four independent variables and 39 in the sample size, a beta is estimated to be
3.98. Using a standard deviation of this beta of 0.87, find the 95% confidence
interval for the beta.
19. Find the regression equation of the following data.
X 
6 
5 
7 
6 
5 
6 
8 
9 
4 
Y 
14 
33 
43 
54 
21 
33 
43 
24 
28 
20. To predict the annual rice yield
in pounds, we use the equation yhat = 859 + 5.76x1 + 3.82x2, where x1 represents the number of acres planted
and where x2 represents the number of acres harvested and where r2 = 0.94.
a. Predict the annual yield when 3,200 acres are planted and 3,000 are
harvested.
b. Interpret the results of r^{2} value.
MATH 533 Week 8  Final Exam Study Guide
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