Assignment

Question 1:

Below are sorted data showing average spending per customer (in dollars) at 74 Noodles & Company restaurants. (a) Construct a frequency distribution. Explain how you chose the number of bins and the bin limits. (b) Make a histogram and describe its appearance. (c) Repeat, using a larger number of bins and different bin limits. (d) Did your visual impression of the data change when you increased the number of bins? Explain.

6.54        6.58        6.58        6.62        6.66        6.70        6.71        6.73        6.75        6.75        6.76        6.76
6.76        6.77        6.77        6.79        6.81        6.81        6.82        6.84        6.85        6.89        6.90        6.91
6.91        6.92        6.93        6.93        6.94        6.95        6.95        6.95        6.96        6.96        6.98        6.99
7.00        7.00        7.00        7.02        7.03        7.03        7.03        7.04        7.05        7.05        7.07        7.07
7.08        7.11        7.11        7.13        7.13        7.16        7.17        7.18        7.21        7.25        7.28        7.28
7.30        7.33        7.33        7.35        7.37        7.38        7.45        7.56        7.57        7.58        7.64        7.65
7.87        7.97                                                                                                                                                       

Question 2:

The contingency table below shows the results of a survey of online video viewing by age. Find the following probabilities or percentages:

a. Probability that a viewer is aged 18-34.
b. Probability that a viewer prefers watching TV videos.
c. Percentage of viewers who are 18-34 and prefer watching user-created videos.
d. Percentage of viewers aged 18-34 who prefer watching user-created videos.
e.Percentage of viewers who are 35-54 or prefer user created-videos.

Question 3:

Prof. Hardtack gave four Friday quizzes last semester in his 10-student senior tax accounting class.

a) Find the mean, median, and mode for each quiz.
b) Do these measures of center agree? Explain.
c) For each data set, note strengths or weaknesses of each statistic of center.
d) Are the data symmetric or skewed? If skewed, which direction?
e) Briefly describe and compare student performance on each quiz.

Quizzes:

• Quiz 1: 60, 60, 60, 60, 71, 73, 74, 75, 88, 99
• Quiz 2: 65, 65, 65, 65, 70, 74, 79, 79, 79, 79
• Quiz 3: 66, 67, 70, 71, 72, 72, 74, 74, 95, 99
• Quiz 4: 10, 49, 70, 80, 85, 88, 90, 93, 97, 98

Question 4:

Calculate the test statistic and p-value for each sample. State the conclusion for the specified α.

a. H0: μ = 200 versus H1: μ ≠ 200, α = .025, x‾=203, s = 8, n = 16
b. H0: μ ≥ 200 versus H1: μ < 200, α = .05, x‾=198, s = 5, n = 25
c. H0: μ ≤ 200 versus H1: μ > 200, α = .05, x‾=205, s = 8, n = 36

Question 5:

Prof. Green gave three exams last semester. Scores were normally distributed on each exam. Below are scores for 10 randomly chosen students on each exam. (a) Find the 95 percent confidence interval for the mean score on each exam. (b) Do the confidence intervals overlap? What inference might you draw by comparing the three confidence intervals?

• Exam 1: 81, 79, 88, 90, 82, 86, 80, 92, 86, 86
• Exam 2: 87, 76, 81, 83, 100, 95, 93, 82, 99, 90
• Exam 3: 77, 79, 74, 75, 82, 69, 74, 80, 74, 76

Question 6:

Daily output of Marathon's Garyville, Lousiana, refinery is normally distributed with a mean of 232,000 barrels of crude oil per day with a standard deviation of 7,000 barrels.

(a) What is the probability of producing at least 232,000 barrels?
(b) Between 232,000 and 239,000 barrels?
(c) Less than 239,000 barrels?
(d) Less than 245,000 barrels?
(e) More than 225,000 barrels?