Statistics for Business Assignment -
Please answer all questions.
Question 1: Prof. Hardtack gave four Friday quizzes last semester in his 10-student senior tax accounting class.
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
(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.
Question 2: In a sample of 100 Planter's Mixed Nuts, 19 were found to be almonds.
(a) Construct a 90 percent confidence interval for the true proportion of almonds.
(b) May normality be assumed? Explain.
(c) What sample size would be needed for 90 percent confidence and an error of ± 0.03?
(d) Why would a quality control manager at Planter's need to understand sampling?
Question 3: Consider the following Excel regression of perceived sound quality as a function of price for 27 stereo speakers.
(a) Is the coefficient of Price significantly different from zero at α = .05?
(b) What does the R2 tell you?
(c) Given these results, would you conclude that a higher price implies higher sound quality?
|
Regression Statistics
|
|
|
R Square
|
0.01104
|
|
Standard Error
|
4.02545
|
|
Observations
|
27
|
|
Statistic
|
Coefficients
|
Std Error
|
t Stat
|
P-value
|
Lower 95%
|
Upper 95%
|
|
Intercept
|
88.4902
|
1.67814
|
52.731
|
0.0000
|
85.0340
|
91.9464
|
|
Price
|
-0.00239
|
0.00453
|
-0.528
|
0.6019
|
-0.01172
|
0.00693
|
Question 4: Suppose a pickup and delivery company states that their packages arrive within two days or less on average. You want to find out whether the actual average delivery time is longer than this. You conduct a hypothesis test.
(a) Set up the null and alternative hypotheses.
(b) Suppose you conclude wrongly that the company's statement about average delivery time is within two days. What type of error is being committed and what is the impact of that error?
(c) Suppose you conclude wrongly that the delivery company's average time to delivery is in fact longer than two days. What type of error did you commit and what is the impact of this error? \
(d) Which error is worse from the company's standpoint, a Type I or a Type II error? Why?
(e) Which error is worse from a consumer standpoint, a Type I or a Type II error? Why?