ASSIGNMENT
1.You want to determine the average number of hours worked by professors at your university per week. You want to be able to express your answer as a confidence interval, with 95% confidence (that is, use z = 1.96) and you are aiming for a precision of plus or minus two hours. Past studies of this type suggest that the variance in professor work hours is about 90 (that is, σ² = 90).
a. How big is the minimum required sample size that would allow you to meet your confidence and precision goals?
b. If you wanted your precision to double (that is, your precision would now be plus or minus one hour), how does that affect your minimum required sample size?
c. c. (Reset precision to the original setting.) If you wanted your confidence to increase to 99% (that is, use z = 2.575 instead of 1.96), how does that affect your minimum required sample size?
2. A publishing house conducted a survey to assess the reading habits of teenagers. The company publishes four types of books specifically tailored to suit the interests of teenagers. Management hypothesizes that there are no differences in the preferences for the four types of books. A sample of 1600 teenagers indicated the following preferences for the four book types.
Publication Frequency of Preference
Non-Fiction 515
Mystery 385
Humor 290
Short Stories 410
TOTAL 1600
Management needs your expertise to determine whether there are differences in preferences for the four types of books. Hint: This problem is the same format as the M&Ms example discussed in class.
a. State the null and alternate hypotheses in plain English sentences (not equations).
b. What is the calculated chi-squared value? Show your calculations.
c. The tabled chi-squared value for 5% significance and three degrees of freedom is 7.81. Can you reject the null hypothesis? Why or why not?
3. Bentley Foods, a large manufacturer of frozen foods, has developed a new line of frozen pizza. Management has agreed to begin producing and marketing the new line if at least 13 percent of the population would prefer the pizza over other frozen pizza currently available. To determine preferences, a sample of 1000 consumers was obtained; 161 indicated that they would prefer the new product over existing brands.
a. State the null and alternate hypotheses.
b. Compute the standard error of the proportion.
c. Calculate the z statistic. Using a 95% significance level, can you reject the null hypothesis? (Hint: for 95% and a one-tailed test, z = 1.645; or for a two-tailed test, z = 1.96.)
4. You believe there may be a relationship between a household's income and whether it possesses more than one car. You have conducted a survey of 100 families and you have discovered the following:
Low income families with one car: 40
Low income families with more than one car: 16
High income families with one car: 15
High income families with more than one car: 29
a. State the null and alternate hypotheses in plain English sentences (not equations).
b. b. What is the calculated chi-squared value? Show your calculations.
c. The tabled chi-squared value for 5% significance and one degree of freedom is 3.84. Can you reject the null hypothesis? Why or why not?