Eh 2550 Dixie State University Confidence Interval for The Population Mean Worksheet

EHS 2550Homework 4
Part I. Worksheets (6 points)
Upload your Week 5 Worksheet and your Week 6 Worksheet.
Part II. Homework questions. (25 points)
Questions 1-10 are required. Questions 11–15 are extra credit. You cannot receive extra credit
unless all required questions are attempted in earnest.
Use the following information to answer questions 1-3: We wish to construct a 95% confidence
interval for the mean weight of newborn elephant calves. Fifty newborn elephants are weighed.
The sample mean is 244 pounds. The sample standard deviation is 11 pounds.
1. Identify the following: (2 points)
a. 𝐱 =
b. σ =
c. n =
2. Construct a 95% confidence interval for the population mean weight of newborn
elephants. State the confidence interval, sketch the graph, and calculate the error bound.
(3 points)
3. What will happen to the confidence interval obtained, if 500 newborn elephants are
weighed instead of 50? Why? (2 points)
Use the following information to answer questions 4-6: The U.S. Census Bureau conducts a
study to determine the time needed to complete the short form. The Bureau surveys 200 people.
The sample mean is 8.2 minutes. There is a known standard deviation of 2.2 minutes. The
population distribution is assumed to be normal.
4. Identify the following: (2 points)
a. 𝐱 =
b. σ =
c. n =
5. Construct a 90% confidence interval for the population meant time to complete the
forms. State the confidence interval, sketch the graph, and calculate the error bound. (3
points)
6. Suppose the Census needed to be 98% confident of the population mean length of time.
Would the census have to survey more people? Why or why not? (2 points)
Use the following information to answer questions 7-8: Suppose the marketing company did do a
survey. They randomly surveyed 200 households and found that in 120 of them, the woman
made the majority of the purchasing decisions. We are interested in the population proportion of
households where women make the majority of the purchasing decisions.
7. Identify the following: (2 points)
a. x =
b. n =
c. p’ =
8. Construct a 95% confidence interval for the population proportion of households where
the women make the majority of the purchasing decisions. State the confidence interval,
sketch the graph, and calculate the error bound. (3 points)
Use the following information to answer question 9: Of 1,050 randomly selected adults, 360
identified themselves as manual laborers, 280 identified themselves as non-manual wage earners,
250 identified themselves as mid-level managers, and 160 identified themselves as executives. In
the survey, 82% of manual laborers preferred trucks, 62% of non-manual wage earners preferred
trucks, 54% of mid-level managers preferred trucks, and 26% of executives preferred trucks.
9. We are specifically interested in the percent of executives who prefer trucks. Construct a
95% confidence interval. State the confidence interval, sketch the graph, and calculate the
error bound. (3 points)
Use the following information to answer questions 10 & 11: A poll of 1,200 voters asked what
the most significant issue was in the upcoming election. Sixty-five percent answered the
economy. We are interested in the population proportion of voters who feel the economy is the
most important.
10. Construct a 90% confidence interval and state the confidence interval and the error
bound. (3 points)
Extra Credit (10 points)
11. What would happen to the confidence interval if the level of confidence were 95%?
Use the following information to answer questions 12-15: The Ice Chalet offers dozens of
different beginning ice-skating classes. All of the class names are put into a bucket. The 5 P.M.,
Monday night, ages 8 to 12, beginning ice-skating class was picked. In that class were 64 girls
and 16 boys. Suppose that we are interested in the true proportion of girls, ages 8 to 12, in all
beginning ice-skating classes at the Ice Chalet. Assume that the children in the selected class are
a random sample of the population.
12. What is being counted?
13. Calculate the following:
a. x =
b. n =
c. p’ = 120/200 =
14. Construct a 99% confidence interval for the true proportion of girls in the ages 8-12
beginning ice-skating classes at the chalet.
15. Label the letters on the graph with the areas, upper and lower limits of the C.I., and the
sample proportion.
A
C
B
D
A=
B=
C=
D=
E=
F=
E
F
EHS 2550
Basic Statistics
Week 5 Worksheet
1. Label the following normal distribution (x = 25, s = 5). Label the mean, 1, 2, and 3 standard deviations
above and below the mean.
2. Label the following standard normal distribution. Label the mean, 1, 2, and 3 standard deviations above
and below the mean.
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3. GRE scores for the year 2019 had a mean verbal score of 497 and a standard deviation of 115. Suppose
you scored a 650. Your standardized score was calculated to be 1.33. Using the z-tables, what percent of
the population who took the GRE did you score higher than?
4. Below is the normal distribution for heights of British men. If a man is 68.2 inches tall, what
percentage of the population is he taller than? What percentage is he shorter than?
Answer Questions 5 and 6 based off of the following frequency curve, which represents the normal
distribution of the variable water bill price (in USD).
148
160
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5. Pretend your water bill is $175. How many standard deviations is this above the mean?
6. Calculate the z-score for a water bill at $175. What percentage of water bills are higher than that?
7. Label the following frequency curve using the Empirical Rule. Label where 68%, 95%, and 99.7% of
the data lie.
8. From 1984 to 1985, the mean height of 15 to 18-year old males from Chile was 172.36 cm, and the
standard deviation was 6.34 cm. Let Y = the height of 15 to 18-year old males in 1984 to 1985. Then Y ~
N(172.36, 6.34).
a) About 68% of the y values lie between what two values? ___________________________. The zscores are ___________________ respectively.
b) About 95% of the y values lie between what two values? ___________________________. The zscores are ___________________ respectively.
c) About 99.7% of the y values lie between what two values? ___________________________. The zscores are ___________________ respectively.
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9. A person scores 3 standard deviations (x = 60, s = 5) above the mean (mean = 45) on a test. What
percentage of the class had a higher score?
10. Two samples are taken from a population. The first sample has n=50 and the second sample has
n=500. Which sample is more likely to have a bell-shaped curve?
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EHS 2550
Basic Statistics
Week 6 Worksheet
1. We want to know the average age of retirement of attorneys in the city of Detroit, MI. We collect a
sample of 100 attorneys from Detroit and calculate the mean age of retirement to be 65 years of age. What
would the purpose of calculating a confidence interval for our results serve? (What information would it
give us?)
2. Below is the results for the example in question 1. Calculate the confidence interval:
3. Write the interpretation for the confidence interval you calculated in question 2.
4. Calculating the confidence interval for a population mean.
You want to determine the mean age of type II diabetes onset. You collect a sample of 300 type II
diabetic patients and calculate the mean age of onset as 48 years of age with a standard deviation of 7.5
years. Calculate the 95% confidence interval for the true population mean.
5. Interpret the confidence interval from question 4.
6. Calculating the confidence interval for a population proportion.
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A professor wants to know what proportion of students in a class have had prior experience using Excel to
graph and preform various statistical tests. She takes a sample of 30 students and finds that 0.65 of
students have prior experience. Calculate a 95% confidence interval for the true population proportion.
7. Interpret the confidence interval from question 6.
8. Calculating the confidence interval for the difference between two means.
You are interested in knowing if students from Oakland University perform better on a standardized exam
than students from Grand Valley State University. Below is the data for each group. Calculate the 95%
confidence interval for the difference of the means.
Oakland University
Grand Valley State University
Mean: 75.5
Mean: 69.8
Standard deviation: 5.40
Standard deviation: 8.56
n: 503
n: 608
9. Interpret the confidence interval from question 8.
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