# A mileage test conducted for a new car model

1. A mileage test is conducted for a new car model, the “Pizzazz.” Thirty (n=30) randomselected Pizzazzes are driven for a month and the mileage is carefully measured in
each. The mean mileage for the sample is 28.6 miles per gallon (mpg) and the
sample standard deviation is 2.2 mpg. Estimate a 95% confidence interval for the
mean mpg in the entire population of Pizzazzes (you might need to round your
answer a little bit to agree with mine).
2. Recent USA TODAY/CNN/Gallup Poll showed that most American people support
encryption on cell phones. The poll of 2000 adults was conducted and 1243 people said
they supported technology companies to provide full encryption in cell phones.
a) Find a 95% confidence interval for people said they supported technology
companies to provide full encryption in cell phones.
b) Perform the hypothesis test for 95 % confidence level that population supports the
full encryption efforts from technology companies.
3. A random sample of 1,562 undergraduates enrolled in marketing courses was asked
to respond on a scale from one (strongly disagree) to seven (strongly agree) to the
proposition: “Advertising helps raise our standard of living.” The sample mean
response was 4.27 and the sample standard deviation was 1.32. Test the hypothesis
that mean score is more than 4.
4. Of a sample of 361 owners of retail service and business firms that had gone into
bankruptcy, 105 reported having no professional assistance prior to opening the
business. Test the null hypothesis with 99 % confidence that at most 25% of all
members of this population had no professional assistance before opening the
5. Pete’s Powerful Pills (PPP) has branched out and is now promoting a vaccine which is
supposed to prevent statisticitis, a nasty disease afflicting students at the local
Evermore University. They are trying to convince the university’s health center that
the vaccine is worth stocking. The campus health center has agreed to stock and
administer the vaccine if it sells well enough, at least µ = 50 vaccines per week. PPP
arranges for the health center to conduct a 36 week trial with the goal of convincing
the center to stock the vaccine. They find that the center has administered an average
of X = 55 vaccines per week over that period with a standard deviation of s = 6.99.
(a) Compute a 95% confidence interval for the mean number of vaccines the health
center will administer per week in the long run. Does it look like the health center
will be willing to stock the vaccine Explain.
(b) Perform the hypothesis test using test statistics that PPP will conduct to convince
the health center the vaccine is worth stocking. In other words, give the null and
alternative hypotheses, both mathematically and in words, and explain your
reasoning.
(c) Suppose that PPP makes a \$5 profit on every vaccine administered by the health
center. Furthermore, suppose they need to average profits of at least \$260 per week
for it to be worthwhile to market the vaccine at the school. Can they be 95% sure of
meeting their goal Explain. (Hint: Use the CI computed in part (a)).
6. A statistics professor used X = “number of class days attended” (out of 30) as an
independent variable to predict Y = “score received on final exam” for a class of his
students. The resulting regression equation was Y = 39.4 + 1.4*X.
Which of the following statements is true
a. If attendance increases by 1.4 days, the expected exam score will increase by 1
point
b. If attendance increases by 1 day, the expected exam score will increase by 39.4
points
c. If attendance increases by 1 day, the expected exam score will increase by 1.4
points
d. If the student does not attend at all, the expected exam score is 1.4.
7. A large class of 360 students has just taken an exam. The exam consisted of 40 truefalse
questions each of which was worth one point. A diligent teaching assistant has
recorded the number of correct answers (Y) and the number of incorrect answers (X)
for each student. Suppose that the student then regresses the variable Y on the
variable X. What will be the values of model b0 (intercept), b1 (slope), R2 to fit to the
data
8. A 95% confidence interval for b1 is determined to be (15,30). Interpret the meaning
of this interval.
a) You can be 95% confident that the mean value of Y will fall between 15 and
30 units.
b) You can be 95% confident that the X value will increase by between 15 and
30 units for every one unit increase in Y.
c) You can be 95% confident that average value of Y will increase by between
15 and 30 units for every one unit increase in X.
d) At the 5% level of significance, there is no evidence of a linear relationship
between Y and X.
9. What do residuals represent
a. The difference between the actual Y values and the mean of Y.
b. The difference between the actual Yvalues and the predicted Y values.
c. The square root of the slope.
d. The predicted value of Y for the average X value.
10. A researcher wants to know if there is a relationship between the number of
shopping centers in a state and the retail sales (in billions \$) of that state. A random
sample of 8 states is listed below. After determining, via a scatter-plot, that the data
followed a linear pattern, the regression line was found. Using the given data and the
given regression output answer the following questions.
State Num Sales
1 630 15.5
2 370 7.5
3 616 13.9
4 700 18.7
5 430 8.2
6 568 13.2
7 1200 23.0
8 2976 87.3
a. What is the equation of the regression line
b. Interpret the slope in the words of the problem.
c. Find r2 and interpret its meaning in the words of the problem.

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