1. A manufacturer wants to increase the shelf life of a line of cake mixes. Past records indicate that the average shelf life of the mix is 216 days. After a revised mix has been developed, a sample of nine boxes of cake mix gave these shelf lives (in days): 215, 217, 218, 219, 216, 217, 217, 218, and 218. Using α = 0.025, has the shelf life of the cake mix increased? What is the computed t and critical t values?
2. What assumption we must make about the population distribution when we conduct a testof hypothesis with small sample?
3. A recent study focused on the number of times men and women send a Twitter message in a day. The information is summarized below.
|
|
Sample Size
|
Sample Mean
|
Population Standard Deviation
|
|
Men
|
25
|
23
|
5
|
|
Women
|
30
|
28
|
10
|
At the .01 significance level, is there a difference in the mean number of times men and women send a Twitter message in a day? What is the p-value for this hypothesis test?
4. What does it indicate if an ANOVA is conducted and the null hypothesis is rejected?
5. Manufacturer of automobile transmissions uses two different processes. Management ordered a study of the production costs to see if there is a difference between the two processes. A summary of the findings is shown next.
|
|
Process 1
|
Process 2
|
Total
|
|
Process Totals ($100s)
|
137
|
108
|
245
|
|
Sample Size
|
10
|
10
|
20
|
|
Sum of Squares
|
1893
|
1188
|
3081
|
What is the critical value of F at the 1% level of significance?
6. In ANOVA, when the null hypothesis is rejected, what conclusion is drawn?
7. An economist is interested in predicting the unemployment rate based on gross domestic product. Is gross domestic product independent or dependent variable? Write an equation that shows the relationship.
8. If the correlation between the two independent variables of a regression analysis is 0.11 and each independent variable is highly correlated to the dependent variable, what action should we take with respect to any of the independent variables from the model?
9. Consider a multiple regression analysis involving 14 independent variables and 150 observations, with SSE = 180 and SS Total = 600. Compute the coefficient of multiple determination.
10. Business cycles that consist of periods of prosperity followed by periods of recession, depression, and recover is an example of what type of time series variation?
11. For the following time series, you are given the moving average forecast.
|
Time Period
2001
2002
|
Time Series Value
19
14
|
3-Year Moving Total
|
|
2003
|
14
|
50
|
|
2004
|
22
|
43
|
|
2005
|
7
|
48
|
|
2006
|
19
|
39
|
|
2007
|
13
|
53
|
|
2008
|
21
|
57
|
|
2009
|
23
|
64
|
|
2010
|
20
|
67
|
|
2011
|
24
|
69
|
|
2012
|
25
|
|
What is the three-year moving average for 2004?
12. The following table shows the sales for a plastics manufacturer recorded over the past year. The seasonal indexes for each quarter are also provided. To track the trend for these four quarters, use the indexes to deseasonalize the sales data.
|
Quarter
|
Sales
|
Index
|
|
1
|
738
|
0.75
|
|
2
|
1012
|
1.04
|
|
3
|
1196
|
1.21
|
|
4
|
962
|
1.00
|
What is the deseasonalized sales value for quarter 3?
13. Discuss the purpose of using a statistical quality control chart?
14. In acceptance sampling, when the incoming lot is accepted?
15. What type of chart is used to identify the relatively few factors that impact the performance of a manufacturing or service process? Provide an example.