Two hundred fifty managers with degrees in business administration indicated their fields of concentration as shown below.
At α = .01 using the p-value approach, test to determine if the position in management is independent of the major of concentration.
In a completely randomized experimental design, 7 experimental units were used for the first treatment, 9 experimental units for the second treatment, and 14 experimental units for the third treatment. Part of the ANOVA table for this experiment is shown below.
(1) Fill in all the blanks in the above ANOVA table. (1% for each blank)
(2) At 95% confidence using both the critical value and p-value approaches, test to see if there is a significant difference among the means.
A regression and correlation analysis resulted in the following information regarding an independent variable (x) and a dependent variable (y).
(1) Develop the least squares estimated regression equation.
(2) At 95% confidence, perform a t test and determine whether or not the slope is significantly different from zero.
(3) Perform an F test to determine whether or not the model is significant. Let α = 0.05 .
(4) Compute the coefficient of determination.
A regression analysis (involving 45 observations) relating a dependent variable (Y) and two independent variables resulted in the following information.
The SSE for the above model is 49. When two other independent variables were added to the model, the following information was provided.
This latter model’s SSE is 40. At 95% confidence test to determine if the two added independent variables contribute significantly to the model.
The following time series shows the number of units of a particular product sold over the past six months.
(1) Compute a 3-month moving average (centered) for the above time series.
(2) Compute the mean square error (MSE) for the 3-month moving average.
(3) Use α = 0.2 to compute the exponential smoothing values for the time series.
(4) Forecast the sales volume for month 7.
Let Ti , i =1, 2, ... , be the inter-arrival times of cars arrive at the gasoline station during busy hours, and a survey shows that Ti are exponentially distributed with rate of 2 cars per minute.
A survey of 200 customers shows that 20 customers feel unsatisfactory for the new product.
(1) What is the 95% confidence interval for the percentage of unsatisfactory customers?
(2) Under the same confidence, how many customers should be surveyed in order that the width of confidence interval is no more than 5%?
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