STATS Lab Activity 9 – Comparing Two Groups

Lab
Activity 9 – Comparing Two Groups

For
question 3, use the FacultySalariesdataset,
obtained from theBulletin of the
American Association of University Professors. The dataset contains the
average male and female salaries (in thousands of dollars) of assistant
professors from 22 different U.S. colleges and universities.

For
question 4,use the Cookiesdataset, which contains the number of chocolate chips
contained in a sample of cookies for 5 different types of chocolate chip
cookies.

1.
(10 pts)For each of the following research questions, please
indicate if the situation or research question involves investigating (a) two
proportions, (b) two means of independent samples, or (c) two
means of paired samples.

A researcher is interested in comparing the resting pulse
rate of people who exercise regularly and people who do not exercise
regularly. Simple random samples of
sixteen people ages 30-40 who do not exercise regularly, and twelve people ages
30-40 who do exercise regularly, are selected and the resting pulse rate of
each person is measured.

A company that designs sports shoes has made an improvement
to their popular running shoe. The company hopes that athletes wearing the new
running shoe will be able to run faster over short distances. To determine
this, the company asks a sample of 35 sprinters to run 100 meters using the old
shoes, and then to run 100 meters using the new shoes. In each case the time it takes to complete
the dash is recorded.

A human resource professional wants to know if there is a
difference in perceived gender equality in his office between men and
women. A random sample containing 47
women and 53 men is taken, and each person is asked, “Do you feel that there is
gender equality in your office?” The responses (“yes” or “no”) are recorded for
each person and the goal is to compare them by gender.

A pharmaceutical company wants to determine whether its new
anti-anxiety medication has any effect on resting pulse rate. It needs to
determine whether the average resting pulse rate for a random sample of 25
adults before the anti-anxiety medication is taken differs from the average
resting pulse rate for the same sample of 25 adults after taking the
anti-anxiety medication.A convenience store manager is curious to know if
caffeinated coffee drinkers are more likely to buy large cups than decaf coffee
drinkers. The store sells only “large”
and “regular” sizes. She selects a
random sample of 30 caffeinated coffee drinkers from her store and records how
many of them buy a large coffee. She
does the same thing for a random sample of 30 decaf coffee drinkers.

2.(Problem 10.10 from the
course text) Two TV commercials are developed for marketing a new product. Group A, consisting of 100 people, watch
commercial A in a controlled setting. A
total of 25 people from Group A say they would buy the product. Group B, also consisting of 100 people, watch
commercial B in a controlled setting.
Just 20 from this group say they would buy the product. The marketing manager concludes that commercial
A is better.

(8 pts) Let p1 =
population proportion of people who would buy the product after watching
commercial A, and p2 = population proportion of people who would buy
the product after watching commercial B.
Identify/calculate the following variables:Sample size of Group
A,n1 =Sample size of Group
B, n2=Number of people in
Group A who would buy the product,x1
=Number of people in
Group B who would buy the product,x2
=Sample proportion of people
who would buy after commercial A,

=
Sample proportion of people
who would buy after commercial B,

=(4 pts)The marketing
manager concludes that commercial A is better.
Test
to see if this conclusion is justified.
In other words, testH0:
p1 – p2 = 0 versusHa: p1 – p2 > 0. Perform the test using softwareand
the some of the values from part a. Paste the output below. Make sure to select the correct alternative
hypothesis!

(2 pts) From the output,
what is the test statistic, z?.0pt;’=”” auto;=”” lfo5;=”” level2=””>(2 pts)What is the p-value?.0pt;’=”” auto;=”” lfo5;=”” level2=””>(6 pts) Based on the p-value, do you believe the
marketing manager’s conclusion is justified?
Why or why not? Answer assuming ? = .10.(6 pts)The 90% confidence
interval for the difference in the proportion of people who would buy the
product after watching commercial A and B is (-0.0470, 0.1470). Explain
how this agrees with your conclusion from the test in part b.

3.
Use
the FacultySalaries
dataset to answer the question, “Is there a difference in the mean male and
female salaries of U.S. university assistant professors?”

(4 pts) Explain why we can
use a paired samples t-test here instead of an independent samples
t-test. Be specific.

Hint: Though many times we use paired samples procedures
when we measure twice on the same subject, we often use it also when
observations in the two samples can be carefully matched together in a logical
way.

(4 pts) Using proper statistical
notation, write down the null and alternative hypothesis for this
test. Define µd = µ1
– µ2, where µ1 is the mean salaries of male assistant
professors (in thousands of dollars) and µ2 is the mean salaries of
female assistant professors (in thousands of dollars).Null
hypothesis: H0:Alterative
hypothesis: Ha:(6 pts) Below are
descriptive statistics for “Males” and for “Females” as obtained from Minitab.
Identify the following values from the output:Sample mean of male
salaries,

=
Sample mean of female
salaries,

=Sample size of each
group, n =Perform, by hand, the hypothesis test you defined in
part b by following the steps
below. Use 95% confidence level (in
other words, ? = .05). Show all work.
(4 pts) Calculate the test
statistic (formula given below). Assume
thatsd = 0.846, and
recall that
.
.0pt;’=”” auto;=”” level2=”” lfo3;=”” l1=””>(2 pts) What are the degrees
of freedom for this test (DF = n– 1)?.0pt;’=”” auto;=”” level2=”” lfo3;=”” l1=””>(6 pts)Use software to find the p-value of the test by following the
instructions below. Don’t forget to
paste the output from the software.Hint:Remember that to the
find the p-value, we have to look at
the alternative hypothesis. In this
case, the alternative hypothesis should be two-sided (“not equal to”), so the p-value = 2*P(T > |t|) = 2*[1 – P(T
< |t|)] or 2*P(T < -|t|) (4 pts)Use software to confirm your test results from part d, and paste the output below. Use it to double-check your results from above.(6 pts) Decide between the null hypothesis and the alternative hypothesis based on the p-value and significance level, ?. Then,write a sentence summarizing the real-world conclusionfrom your test. Make sure your conclusion is specific and clear. 4. Use the Cookies dataset to answer the question, “Do reduced fat Chips Ahoy chocolate chip cookies contain fewer chocolate chips on average than regular Chips Ahoy chocolate chip cookies?” We’ll assume 99% confidence (so ? = .01). (4 pts) Complete the correct notation for the null and alternative hypotheses for this test by filling in the two blanksbelow with either =, ?, <, or >. Note that µ1 is be the mean number
of chocolate chips in reduced fat Chips Ahoy and µ2 is the mean number
of chocolate chips in regular Chips Ahoy.Null
hypothesis: H0: ?1 –
?2 ___ 0Alterative
hypothesis: Ha: ?1 –
?2 ___ 0(4 pts) Because the data
come from independent samples (instead of paired samples), we should perform an
independent two-sample t-test. However,
should we perform a pooled or unpooled test? Show how you
came to this conclusion. Note that
sample standard deviation of chocolate chips in reduced fat cookies iss1= 2.5515 and the sample
standard deviation of chocolate chips in regular cookies iss2 = 3.8351.Hint: If

,
use pooled (assume equal variances/standard deviations). Otherwise, use unpooled.(4 pts)Use softwareto
perform the test from part a and
paste the output below. Make sure to
select the correct alternative hypothesis and the correct test (pooled vs.
unpooled).

(2 pts) From the output,
what is the test statistic, t?.0pt;’=”” auto;=”” lfo5;=”” level2=””>(2 pts)What is the p-value?.0pt;’=”” auto;=”” lfo5;=”” level2=””>(6 pts) Based on the p-value, would you conclude that
there are fewer chocolate chips in reduced fat vs. regular Chip Ahoy chocolate
chip cookies? Why or why not?