
Concept explainers
a.
To state: The hypothesis.
a.

Answer to Problem 15E
The hypothesis for interaction is,
The hypothesis for age of salespersonis,
The hypothesis for product is,
Explanation of Solution
Given info:
The table shows age of the sales representative and type of item affect monthly sales.
Calculation:
The hypothesis for interaction is,
Null hypothesis:
Alternative hypothesis:
The hypothesis for age of salesperson is,
Null hypothesis:
Alternative hypothesis:
The hypothesis for productis,
Null hypothesis:
Alternative hypothesis:
b.
To find: The critical value for each F test.
b.

Answer to Problem 15E
The critical F-value of A is 4.26.
The critical F-value of B and
Explanation of Solution
Given info:
The level of significance is 0.05.
Calculation:
Consider factors A represent the type of paintand B represents the geographic location.
Here,
The formula to find the degrees of freedom for factor A is,
Thus, the degrees of freedom for factor A is1.
Here,
The formula to find the degrees of freedom for factor B is,
Thus, the degrees of freedom for factor B is3.
The formula to find the degrees of freedom for factor
Thus, the degrees of freedom for factor
The degrees of freedom for the within (error) factor
The degrees of freedom for the within (error) factor is 24.
Critical value:
Here A having 1 degrees of freedom and B and
For A:
The critical F-value of A is obtained using the Table H: The F-Distribution with the level of significance
Procedure:
- Locate 24 in the degrees of freedom, denominator row of the Table H.
- Obtain the value in the corresponding degrees of freedom, numerator column below 1.
That is,
Thus, the critical F-value of A is 4.26.
For B and
The critical F-value of B and
Procedure:
- Locate 24 in the degrees of freedom, denominator row of the Table H.
- Obtain the value in the corresponding degrees of freedom, numerator column below 2.
That is,
Thus, the critical F-value of B and
Decision criteria:
If
If
If
c.
To compute: The summary table.
To find: The test value.
c.

Answer to Problem 15E
The summary table is,
The test valuesare 1.57, 8.21 and 37.09.
Explanation of Solution
Calculation:
Software procedure:
Step-by-step procedure to obtain the test statistics and P-value using the MINITAB software:
- Choose Stat > ANOVA > Two-Way.
- In Response, enter the column of Sales.
- In Row Factor, enter the column of Ages of sales person.
- In Column Factor, enter the column of product.
- Click OK.
Output using the MINITAB software is given below:
From Minitab output, the test valuesare 1.57, 8.21 and 37.09.
d.
To make: The decision.
d.

Answer to Problem 15E
The null hypothesis is rejected for
Explanation of Solution
Conclusion:
From the result of part (c), the
Decision for
Here, the test value of
That is,
Thus, it can be concluding that, the null hypothesis for
Decision for
Here, the test value of
That is,
Thus, it can be concluding that, the null hypothesis for
Decision for
Here, the test value of
That is,
Thus, it can be concluding that, the null hypothesis for
e.
To explain: The results.
e.

Answer to Problem 15E
The result concludes that, there is an interception effect between the ages of salespeople and the type of products sold.
Explanation of Solution
Calculation:
From the results, it can be observed there is a significant between the ages of the sales people and the products they sell on the monthly sales.
Here, the integration effect is between the ages of the sales person and the type of product sold. So, the procedure for drawing the graph for the interaction plot is given below.
Minitab Procedure:
- Choose Stat > ANOVA >Interaction Plot.
- In Response, enter the column of Sales.
- In Factors, enter the column of Ages of sales person and product.
- Click OK.
Output using the MINITAB software is given below:
Interpretation:
From the graph, it can be observed that the lines cross. So, the interaction is disordinal interaction. Hence there is an interception effect between the ages of salespeople and the type of products sold.
Want to see more full solutions like this?
Chapter 12 Solutions
Loose Leaf for Elementary Statistics: A Step By Step Approach
- Consider an event X comprised of three outcomes whose probabilities are 9/18, 1/18,and 6/18. Compute the probability of the complement of the event. Question content area bottom Part 1 A.1/2 B.2/18 C.16/18 D.16/3arrow_forwardJohn and Mike were offered mints. What is the probability that at least John or Mike would respond favorably? (Hint: Use the classical definition.) Question content area bottom Part 1 A.1/2 B.3/4 C.1/8 D.3/8arrow_forwardThe details of the clock sales at a supermarket for the past 6 weeks are shown in the table below. The time series appears to be relatively stable, without trend, seasonal, or cyclical effects. The simple moving average value of k is set at 2. What is the simple moving average root mean square error? Round to two decimal places. Week Units sold 1 88 2 44 3 54 4 65 5 72 6 85 Question content area bottom Part 1 A. 207.13 B. 20.12 C. 14.39 D. 0.21arrow_forward
- The details of the clock sales at a supermarket for the past 6 weeks are shown in the table below. The time series appears to be relatively stable, without trend, seasonal, or cyclical effects. The simple moving average value of k is set at 2. If the smoothing constant is assumed to be 0.7, and setting F1 and F2=A1, what is the exponential smoothing sales forecast for week 7? Round to the nearest whole number. Week Units sold 1 88 2 44 3 54 4 65 5 72 6 85 Question content area bottom Part 1 A. 80 clocks B. 60 clocks C. 70 clocks D. 50 clocksarrow_forwardThe details of the clock sales at a supermarket for the past 6 weeks are shown in the table below. The time series appears to be relatively stable, without trend, seasonal, or cyclical effects. The simple moving average value of k is set at 2. Calculate the value of the simple moving average mean absolute percentage error. Round to two decimal places. Week Units sold 1 88 2 44 3 54 4 65 5 72 6 85 Part 1 A. 14.39 B. 25.56 C. 23.45 D. 20.90arrow_forwardThe accompanying data shows the fossil fuels production, fossil fuels consumption, and total energy consumption in quadrillions of BTUs of a certain region for the years 1986 to 2015. Complete parts a and b. Year Fossil Fuels Production Fossil Fuels Consumption Total Energy Consumption1949 28.748 29.002 31.9821950 32.563 31.632 34.6161951 35.792 34.008 36.9741952 34.977 33.800 36.7481953 35.349 34.826 37.6641954 33.764 33.877 36.6391955 37.364 37.410 40.2081956 39.771 38.888 41.7541957 40.133 38.926 41.7871958 37.216 38.717 41.6451959 39.045 40.550 43.4661960 39.869 42.137 45.0861961 40.307 42.758 45.7381962 41.732 44.681 47.8261963 44.037 46.509 49.6441964 45.789 48.543 51.8151965 47.235 50.577 54.0151966 50.035 53.514 57.0141967 52.597 55.127 58.9051968 54.306 58.502 62.4151969 56.286…arrow_forward
- The accompanying data shows the fossil fuels production, fossil fuels consumption, and total energy consumption in quadrillions of BTUs of a certain region for the years 1986 to 2015. Complete parts a and b. Year Fossil Fuels Production Fossil Fuels Consumption Total Energy Consumption1949 28.748 29.002 31.9821950 32.563 31.632 34.6161951 35.792 34.008 36.9741952 34.977 33.800 36.7481953 35.349 34.826 37.6641954 33.764 33.877 36.6391955 37.364 37.410 40.2081956 39.771 38.888 41.7541957 40.133 38.926 41.7871958 37.216 38.717 41.6451959 39.045 40.550 43.4661960 39.869 42.137 45.0861961 40.307 42.758 45.7381962 41.732 44.681 47.8261963 44.037 46.509 49.6441964 45.789 48.543 51.8151965 47.235 50.577 54.0151966 50.035 53.514 57.0141967 52.597 55.127 58.9051968 54.306 58.502 62.4151969 56.286…arrow_forwardThe accompanying data shows the fossil fuels production, fossil fuels consumption, and total energy consumption in quadrillions of BTUs of a certain region for the years 1986 to 2015. Complete parts a and b. Develop line charts for each variable and identify the characteristics of the time series (that is, random, stationary, trend, seasonal, or cyclical). What is the line chart for the variable Fossil Fuels Production?arrow_forwardThe accompanying data shows the fossil fuels production, fossil fuels consumption, and total energy consumption in quadrillions of BTUs of a certain region for the years 1986 to 2015. Complete parts a and b. Year Fossil Fuels Production Fossil Fuels Consumption Total Energy Consumption1949 28.748 29.002 31.9821950 32.563 31.632 34.6161951 35.792 34.008 36.9741952 34.977 33.800 36.7481953 35.349 34.826 37.6641954 33.764 33.877 36.6391955 37.364 37.410 40.2081956 39.771 38.888 41.7541957 40.133 38.926 41.7871958 37.216 38.717 41.6451959 39.045 40.550 43.4661960 39.869 42.137 45.0861961 40.307 42.758 45.7381962 41.732 44.681 47.8261963 44.037 46.509 49.6441964 45.789 48.543 51.8151965 47.235 50.577 54.0151966 50.035 53.514 57.0141967 52.597 55.127 58.9051968 54.306 58.502 62.4151969 56.286…arrow_forward
- For each of the time series, construct a line chart of the data and identify the characteristics of the time series (that is, random, stationary, trend, seasonal, or cyclical). Month PercentApr 1972 4.97May 1972 5.00Jun 1972 5.04Jul 1972 5.25Aug 1972 5.27Sep 1972 5.50Oct 1972 5.73Nov 1972 5.75Dec 1972 5.79Jan 1973 6.00Feb 1973 6.02Mar 1973 6.30Apr 1973 6.61May 1973 7.01Jun 1973 7.49Jul 1973 8.30Aug 1973 9.23Sep 1973 9.86Oct 1973 9.94Nov 1973 9.75Dec 1973 9.75Jan 1974 9.73Feb 1974 9.21Mar 1974 8.85Apr 1974 10.02May 1974 11.25Jun 1974 11.54Jul 1974 11.97Aug 1974 12.00Sep 1974 12.00Oct 1974 11.68Nov 1974 10.83Dec 1974 10.50Jan 1975 10.05Feb 1975 8.96Mar 1975 7.93Apr 1975 7.50May 1975 7.40Jun 1975 7.07Jul 1975 7.15Aug 1975 7.66Sep 1975 7.88Oct 1975 7.96Nov 1975 7.53Dec 1975 7.26Jan 1976 7.00Feb 1976 6.75Mar 1976 6.75Apr 1976 6.75May 1976…arrow_forwardHi, I need to make sure I have drafted a thorough analysis, so please answer the following questions. Based on the data in the attached image, develop a regression model to forecast the average sales of football magazines for each of the seven home games in the upcoming season (Year 10). That is, you should construct a single regression model and use it to estimate the average demand for the seven home games in Year 10. In addition to the variables provided, you may create new variables based on these variables or based on observations of your analysis. Be sure to provide a thorough analysis of your final model (residual diagnostics) and provide assessments of its accuracy. What insights are available based on your regression model?arrow_forwardI want to make sure that I included all possible variables and observations. There is a considerable amount of data in the images below, but not all of it may be useful for your purposes. Are there variables contained in the file that you would exclude from a forecast model to determine football magazine sales in Year 10? If so, why? Are there particular observations of football magazine sales from previous years that you would exclude from your forecasting model? If so, why?arrow_forward
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillBig Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt

