1. A mileage test is conducted for a new car model, the "Pizzazz." Thirty (n=30) random selected 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 business:
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 true- false 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 Y values 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.