MATH 534 Applied Managerial Statistics
MATH 534 Week 8 Final Exam Solution’s Guide (Summer 2025)
1. Question: The following numbers represent the weights in pounds of six 7-year old children in
Mrs. Jones’ second gr
...
MATH 534 Applied Managerial Statistics
MATH 534 Week 8 Final Exam Solution’s Guide (Summer 2025)
1. Question: The following numbers represent the weights in pounds of six 7-year old children in
Mrs. Jones’ second grade class (25, 60, 51, 47, 49, 45). Find the mean, median, mode, variance,
and standard deviation.
2. Question: If the variance is 846, what is the standard deviation?
3.Question: 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. Question: For two events, C and D, P(C) = 0.6, P(D)=0.3, and P(C|D) = 0.2. Find P(CÇD).
Question: If a binomial variable has n=34 and p=0.30, Õnd the mean, variance, and standard
deviation.
5.
Question: 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.
6.
Question: 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?
7.
Question: 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?
8.
Question: On a dry surface, the braking distance (in meters) of a certain caris a normal
distribution with mu = μ= 45.1 m and sigma = σ= 0.5. (1). Find the braking distance that
represents the 91st percentile. (2). Find the probability that the braking distance is less than
orequal to 45 m. (3). Find the probability that the braking distance is greater than46.8 m… Find
the probability that the braking distance is between 45 mand 46.8 m.
9.
Question: A sample of 58 days of gas prices has a mean of $2.75 and a standard deviation of
$0.86. Construct the 95% conÕdence interval.
10.
Question: 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 Õnd 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. (1). Find a 99% conÕdence interval for the true
mean heart rate of all people with this untreated condition. Show your calculations.
(2). Interpret this conÕdence interval, and write a sentence that explains it.
11.
Question: Determine the minimum required sample size if you want to … 80% conÕdent that
the sample mean is within 2 units of the population mean given sigma = 9.4. Assume the
population is normally distributed.
12.
Question: 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% conÕdence interval. A previous study estimated
the population proportion at 0.21. (1). Using this previous study as an estimate for p, what
sample size should be used?. (2). If the previous study was not available, what estimate for p
should … used?
13.
Question: 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 p-value, conclusion, and implication for the claim.
14.
Question: 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 26.7 mph and a
standard deviation of 3.9 mph. Do the neighbors have enough information to support their
claim at an alpha of 0.05? Write the hypotheses, the p-value, conclusion, and implication for the
claim.
Question: A doctor claims that 30% of patients only have a cold. During one month, the doctor
Õnds that 112 of 420 patients only has a cold. At α=0.06, can the doctor support the claim?
Write the hypotheses, the p-value, conclusion, and implication for the claim.
16.
Question: To test if there was a positive relationship between the dependent and independent
variables, a hypothesis test found a t-statistic 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?
17.
Question: In a multiple regression with four independent variables and 39 in the sample size, a
beta is … 3.98. Using a standard deviation of this beta of 0.87, Õnd the 95% conÕdence interval
for the beta.
18.
19. Question: Find the regression equation of the following data.
Question: To predict the annual rice yield in pounds, we use the equation y-hat= 859 + 76x1 +
3.82x2,where x1 represents the number of acres planted and where x2 represents the number
of acres harvested and where r = 0.94. (1). Predict the annual yield when 3,200 acres are …
and 3,000 are … (2). Interpret the results of r
20.
Question: If a regression model is that y-hat = 5.4×1 – 3×2 + 10, interpret the meaning of the
slopes.
21. Question: If a regression model is that y-hat = 5.4×1 – 3×2 + 10, interpret the meaning of the
slopes
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