Assignment 3 – Business Faculty – Summer Semester
Professor: Dr. Rosa Padilla de Casamayor
Follow the procedures covered in this chapter to generate appropriate to answer the following questions:
Review problems of chapter
Follow the procedures covered in this chapter to generate appropriate to answer the following questions: 1. What necessary assumption must be met for an analysis of variance test to be valid?
2. In a One-way ANOVA, is the Sig or p_value is greater than the level of significance, you: a. Reject Ho because there is evidence all the means differ
b. Reject Ho because there is evidence at least one of the means differs from the others c. Do not reject Ho because there is no evidence of a difference in the means
d. Do not reject Ho because one mean is different from the others
3. In a one-way ANOVA, if the F test statistics is greater than the critical F value, you: a. Reject Ho because there is evidence all the means differ
b. Reject Ho because there is evidence at least one of the means differs from the others c. Do not reject Ho because there is no evidence of a difference in the means
d. Do not reject Ho because one mean is different from the others 4. In a one-way ANOVA, the null hypothesis is always:
a. All the population means are different b. Some of the population means are different c. Some of the population means the same d. All of the population means are the same
The following should be used to answer Question 6 through 9
5. For fast-food restaurants, the drive through window is an increasing source of revenue. The chain that offers that fastest service is considered most likely to attract additional customers. In a study of 20 drive-through times (from menu board to departure) at 4 fast-food chains, the following ANOVA table was developed.
ANOVA
Sum of
Squares df
Mean
Square F
Between Groups 6536 3 13.35
Within Groups 76 163.25
Total 18943 79
Referring to the preceding table,
a. Between Groups degrees of freedom is:______ _____ b. What was the overall sample size:______ _____ c. How many groups were there? :______ _____
f. Find the critical value of F and P_value:______ _____
g. Referring to the preceding table, at the 5% level of significance you:
a. Do not reject the null hypothesis and conclude that no difference exists in the mean drive-up time between the fast-foot chains
b. Reject the null hypothesis and conclude that a difference exists in the mean drive-up time between the fast-foot chains c. Do not reject the null hypothesis and conclude that a difference exists in the mean drive-up time between the fast-foot
chains
d. Reject the null hypothesis and conclude that no difference exists in the mean drive-up time between the fast-foot chains
6. Sales of people magazine are compared over a 5-week period at four borders outlets in Egypt. Do the data show a significance difference in mean weekly sales?
Weekly sales
Store 1 Store 2 Store 3 Store 4
102 97 89 100
106 77 91 116
105 82 75 87
115 80 106 102
112 101 94 100
a. Are the differences statistically significant? (Conduct ANOVA test).
ANOVA
Mean weekly sales
Sum of Squares df Mean Square F Sig.
Between Groups 1325.350 3 441.783 4.709 .015
Within Groups 1501.200 16 93.825
Total 2826.550 19
b. If F is significant, which group(s) is (are) significantly different from which? (See Multiple comparison)
Multiple Comparisons
Dependent Variable: Mean weekly sales
Tukey HSD
(I) Store (J) Store Mean Difference (I-J)
Std. Error Sig. 95% Confidence Interval
Lower Bound Upper Bound
Store 1 Store 2 20.60000* 6.12617 .019 3.0729 38.1271
Store 4 7.00000 6.12617 .670 -10.5271 24.5271
Store 2
Store 1 -20.60000* 6.12617 .019 -38.1271 -3.0729
Store 3 -3.60000 6.12617 .934 -21.1271 13.9271
Store 4 -13.60000 6.12617 .160 -31.1271 3.9271
Store 3
Store 1 -17.00000 6.12617 .059 -34.5271 .5271
Store 2 3.60000 6.12617 .934 -13.9271 21.1271
Store 4 -10.00000 6.12617 .389 -27.5271 7.5271
Store 4
Store 1 -7.00000 6.12617 .670 -24.5271 10.5271
Store 2 13.60000 6.12617 .160 -3.9271 31.1271
Store 3 10.00000 6.12617 .389 -7.5271 27.5271
*. The mean difference is significant at the 0.05 level.
c. What is the independent or factor variable? d. What is the data scale of the independent variable? e. What is the dependent variable?
f. What is the data scale of the dependent variable?
7. Uwumuremyi Methode, vice president of Kigali Bank, is reviewing employee performance for possible salary increases. In evaluating tellers, Methode decides that an important performance criterion is the number of customers served each day. He expects that each teller should handle approximately the same number of customer daily. Otherwise, each teller should be rewarded or penalized accordingly. How does Method compare the tellers? Or in another hands, at least one of the tellers is likely to be handling more or less customers than the others. Answer: F=3.78, sig=.047
Customer Traffic Data
Teller 1 Teller 2 Teller 3
45 55 54
56 50 61
47 53 54
51 59 58
50 58 52
45 49 51
Basic assumptions for the analysis of variance and normality (interpret all the following tables)
Test of Homogeneity of Variances
Levene Statistic df1 df2 Sig.
Ho:
Ha:
Sig.
Making decision and interpret the result:
Tests of Normality
Teller Kolmogorov-Smirnova Shapiro-Wilk
Statistic df Sig. Statistic df Sig.
Number of customer
Teller 1 .181 6 .200* .904 6 .400
Teller 2 .169 6 .200* .933 6 .602
Teller 3 .271 6 .193 .914 6 .466
*. This is a lower bound of the true significance.
Ho:
Ha:
Sig.
Making decision and interpret the result:
8. A random sample of 15 nations from three levels of development has been selected. “Least developed” nations are largely agricultural and have two lowest quality of life. “Developed” nations are industrial and the most affluent and modern. “Developing” nations are between these extremes. Are these general characteristics reflected in differences in life expectancy (the number of years the average citizen can expect to live at birth) between the three categories? The data for 15 nations:
Least developed Developing Developed
Nation Life expectancy Nation
Life
expectancy Nation
Life expectancy
Cambodia 56.8 China 71.6 Australia 79.9
Mali 47 Indonesia 68.3 Belgium 78
Nepal 58.2 Pakistan 61.5 Japan 80.8
Niger 41.6 South Korea 74.7 Russia 67.3
Sudan 56.9 Turkey 71.2 United Kingdom 77.8
Source: U.S. Bureau of the census 2003. Statistica Abstract of the United States, 2002. P. 829. Washington,
D.C.: U.S. Government Printing Office.
ANOVA
Life_Expectancy
Sum of Squares df Mean Square F Sig.
Between Groups 1604.625 2 802.313 22.048 .000
Within Groups 436.664 12 36.389
Total 2041.289 14
9. Suppose the National Transportation Safety Board (NTSB) wants to examine the safety of compact cars, midsize cars, and full-size cars. It collects a sample of three for each of the treatments (cars types). Using the hypothetical data provided below, test whether the mean pressure applied to the driver’s head during a crash test is equal for each types of car. Use α = 5%.
Determining Which Mean(s) Is/Are Different Compact cars Midsize cars Full-size cars
643 469 484
655 427 456
702 525 402
a. The mean head pressure is statistically equal across the three types of cars. Output from SPSS
ANOVA
The mean head pressure
Sum of Squares df Mean Square F Sig.
Between Groups 86049.556 2 43024.778 25.175 .001
Within Groups 10254.000 6 1709.000
Total 96303.556 8
b. Check Multiple comparison
Dependent Variable: The mean head pressure
Tukey HSD
(I) Types of cars (J) Types of cars Mean Difference (I-J)
Std. Error Sig. 95% Confidence Interval
Lower Bound Upper Bound
Compact cars
Midsize cars 193.00000* 33.75401 .003 89.4334 296.5666
Full-size cars 219.33333* 33.75401 .002 115.7668 322.8999
Midsize cars
Compact cars -193.00000* 33.75401 .003 -296.5666 -89.4334
Full-size cars 26.33333 33.75401 .728 -77.2332 129.8999
Full-size cars
Compact cars -219.33333* 33.75401 .002 -322.8999 -115.7668
Midsize cars -26.33333 33.75401 .728 -129.8999 77.2332
*. The mean difference is significant at the 0.05 level.
c. Check Homogeneous Subsets
The mean head pressure
Tukey HSD
Types of cars N Subset for alpha = 0.05
1 2
Full-size cars 3 447.3333
Midsize cars 3 473.6667
Compact cars 3 666.6667
Sig. .728 1.000
Means for groups in homogeneous subsets are displayed.
e. Check the assumption about homogeneity of variances
Test of Homogeneity of Variances
The mean head pressure
Levene Statistic df1 df2 Sig.
