STAT 354 sections 001 – Homework Assignment A Spring 2019
Due Date: March 4
th in class
You need to turn in a hard copy of your solutions and all pages need to be stapled together
You are required to work alone on these questions. Any share of work or discussing specific
questions with other students is not allowed. I take any violations seriously. Anyone who fails
to follow the academic integrity rules will be reported after receiving a zero for the assignment.
You are only allowed to discuss your questions with the instructor of the course or the GTA.
All 14 questions need to be completely answered and written or typed *in order*
Remember, for all hypothesis tests, 5 steps needs to be clearly specified and completed in detail.
1. One attorney claims that more than 25% of all the lawyers in Boston advertise for their
business. A sample of 200 lawyers in Boston showed that 63 of the lawyers had used
some form of advertising for their business. At 𝛼 =0.05, is there enough evidence to
support the attorney’s claim? Use the P-value method to test this hypothesis.
2. Results of a survey conducted in 15 large cities within the U.S. finds that the average
commute time one way to/from work is 25.4 minutes. An executive of chamber of
commerce believes that the commute time in her city is less than the amount reported by
the survey. She randomly selects 25 commuters from her city and finds the average is
22.1 minutes and the standard deviation is 5.3 minutes. At 𝛼 = 0.10, is her claim correct?
3. A nutritionist claims that the number of calories that exist in one teaspoon of a specific
brand of maple syrup has a standard deviation of 60. He selects a sample of 18 maple
syrups from that brand. Number of calories is shown. At 𝛼 =0.1, is the claim rejected?
53, 210, 100, 200, 100, 220, 210, 100, 240, 200, 100, 210, 100, 210, 100, 210, 100, 60
You may use R to calculate the mean and standard deviation of the data above.
(Remember, sd() can be used in R to calculate the standard deviation of a vector or
4. What two assumptions must be met when you are using the z test to test differences
between two means? Write both of them.
5. Men are believed to have a slightly longer average length of short hospital stays than
women; 5.2 days versus 4.5 days respectively. A random sample of short hospital stays
for men and women showed the following. At 𝛼 =0.01, is there enough evidence to
conclude the average short hospital stay for men is indeed longer than that for women?
6. Two brands of AAA batteries are tested in order to compare their voltage. The data
summary can be found below. Find the 95% confidence interval of the true difference in
the means of their voltage. Assume that both variables are normally distributed.
7. At a PGA tournament, held in Florida, the following scores from two consecutive
weekdays were revealed for eight randomly selected golfers. At 𝛼 =0.05, is there
significant evidence that there is a difference in mean scores of golfers for the two days?
8. A recent health report revealed that a woman with insurance spends an average of 2.3
days in the hospital following a routine childbirth, while a woman without insurance
spends an average of 1.9 days at the hospital. Two samples of 16 women each were used
in both samples. The standard deviation of the first sample is equal to 0.6 day, and the
standard deviation of the second sample is 0.3 day. At 𝛼 =0.01, test the claim that the
means are equal. Find the 99% confidence interval for the differences of the means and
compare the result of the hypothesis test to the one for the confidence interval.
9. In a random sample of 50 men, 44 of them said they had less leisure time now compared
to 10 years ago. In a random sample of 50 women, 48 women said that they had less
leisure time now than 10 years ago. At 𝛼 =0.10 is there a significant difference between
the two proportion? Find the 90% confidence interval for the difference of the two
proportions. Does the confidence interval contain 0? If yes, what dose it mean?
10. An architect claims that the variance of heights of tall buildings in Denver, CO is the
same as the variance in heights of tall buildings in Detroit, MI. At 𝛼 =0.10 test his claim.
11. Respond to each of the following questions using this partially completed one-way
a. How many different populations are being compared?
b. Fill in the ANOVA table with the missing values.
c. State the appropriate null and the alternative hypothesis.
d. Based on the analysis of variance F-test, what conclusion
should be reached regarding the null hypothesis?
Test Using an 𝛼= 0.05.
First report the critical value (you may use R command
qf(1-𝛼, dfN, dfD) to find the F critical value, then compare it to the F test-statistics, and
write down the decision you make).
12. The numbers of farms per state are found in three sections of the U.S. and reported below
(in thousands). At a 𝛼 = 0.05, test the claim of a farmer that the location does not matter
and the mean number of farms is the same across these three divisions. Show all of your
calculations by hand step by step (R or other software cannot be used for this question).
13. A data set named “EXERCISE” is given to you (posted on Blackboard).
Rows: It includes 40 individuals; the pulse of each of 40 people was taken, before and
after running one mile.
Columns in order: The variables include their ‘ID’, their ‘SEX’ where 1 represents male
and 2 represents female, ‘SMOKE’ where 0 means they don’t smoke and 1 means they
smoke, ‘AGE’ showing the age of individuals, ‘PULSE_1’ showing the pre-exercise
pulse, ‘PULSE_2’ showing the post-exercise pulse rate, and finally the last column
‘NAME’ includes the names of the individuals participating in this study.
a. Read the data into R or R-studio and report the summary of the data for all variables. R
command to get the summary followed by output without the change of format should be
pasted in your document.
b. Using the proper statistical test, compare the pulse rate of individuals before and after
running one mile. The test should be conducted in R.
i. Explain why this test (name the test you are using) was being chosen.
ii. Write down the null and alternative hypothesis to see whether there is a difference
between the average pulse rates before and after running one mile. (𝛼 = 0.05)
iii. Using the appropriate R code, perform the test (the code used to test this
hypothesis needs to be included in your output)
iv. Pasting the output R gave you here, explain what your decision is regarding this
hypothesis. Also, write down the interpretation/conclusion in one sentence.
c. Testing for the effect of ‘SEX’ and ‘SMOKE’ and their interaction effect, perform a test
to see whether there is a difference in the mean of ‘PULSE_2’ (the post-exercise pulse
rate) based on individuals’ sex and whether or not they smoke.
i. What test should you use? Explain why this test was being chosen.
ii. Write down the null and alternative hypotheses for the tests of main and
interaction effects. (𝛼 = 0.05)
iii. Using the appropriate R code, perform the test (the code used to test this
hypothesis needs to be included in your output).
iv. Pasting the output R gave you here, explain what your decisions are regarding the
three hypotheses you tested for. You need to explain what part of the output led
you to the conclusion you made. Also, write own the interpretation for each
hypothesis in one sentence.
14. General Electric recently conducted a study to evaluate filaments in their industrial high
intensity bulbs. Investigators recorded the number of weeks each high-intensity bulb
would last before failure for three test filaments (Groups 1, 2, and 3) and the standard
filament (Group 4). The results are as follows. Using 𝛼 = 0.01,
Group 1 2 3 4
15 14 25 28
18 18 19 31
21 20 22 27
16 16 20 32
17 15 18 23
20 16 24 25
18 22 27 30
14 18 27
a. Write an appropriate ANOVA hypothesis to test the difference in means of the four
groups (null and alternative).
b. Read the data into R or R-studio, run an ANOVA model in R and paste the code used as
well as the output here. What is the decision based on the ANOVA test? You need to
explain what part of the output led you to the conclusion you made.
c. Continue using R: Use the Tukey method to test all pairwise contrasts. Show the R code,
output, and explain the results of all the comparisons in complete sentences while
referencing the parts/numbers on the output that support your conclusions.