Statistics Unit 4
Statistics Unit 9 Lincoln College Online Staci Morris
Statistics Unit 9
Page 581-584 #4, 5, 7, 15, and 18
4.) Describe the hypotheses for a two way ANOVA test.
Two way ANOVA Test will have three null hypotheses. One hypothesis will represent the independent variable, and its effects on the second hypothesis which is the dependent variable (main effect). The third null hypothesis is the interaction effect on both independent variables on the dependent variable.
5.) The table shows the cost per ounce (in dollars) for a random sample of toothpastes exhibiting very good stain removal, good stain removal, and fair stain removal. At a = 0.05, can you conclude that the mean costs per ounce are different? …show more content…
a.) Hₒ: μ¹ = μ² = μᶟ Hₐ: Claim- one mean is seen as being different from the others.
b.) Fₒ = 3.37 Rejection Region F > 3.37 c.) 1.02 d.) Fail to reject the Hₒ
e.) Evidence is not enough at 5% significance level to determine if the mean cost per ounce is different.
7.) The table shows the salaries (in thousands of dollars) of randomly selected individuals from the federal, state, and local levels of government. At a = 0.01, can you conclude that at least one mean salary is different? a.) Hₒ: μ¹ = μ² = μᶟ Hₐ: Claim- one mean is different from the others b.) Fₒ = 5.49 Rejection Region F > 5.49 c.) 22.99 d.) Reject Hₒ
e.) There is evidence at 1% significance level to determine that at least one mean salary is different.
15.) Table shows the number of female students who played on a sports team in grades 9 through 12 for a random sample of 8 high schools in a state. At a 0.01, can you reject the claim that the mean numbers of female students who played on a sports team are equal for all grades?
Analysis of Variance:
Column
Means
Column n Mean Standard Error
Grade 9 8 84.375 9.531784
Grade 10 8 79.25 9.090321
Grade 11 8 76.625 7.648383
Grade 12 8 70.75 6.9224014
ANOVA Table
Source df ss ms
Treatments 3 771.25 257.08334
Error 28 1574.75 559.8125
Total 31 16446
F-Stat P-Value
0.45923114 0.7129
P = 0.7129 > 0.01 It failed to reject Hₒ. Not enough evidence at 1% significance level that rejects the claim. Female student mean numbers are the same in every grade.
18.) The owner of a car dealership wants to determine if the gender of sales person and the type of vehicle sold affect the number of vehicles sold in a month. The block design shows the number of vehicles, listed by type, sold in a month by a random sample of eight sales people.
Reject the null hypothesis. The number of sales by a gender does have an effect on the sales of vehicles sold. There is a significance level of evidence to support the rejection. Reference
Larson, Ron and Farber, Betsy. (2012.). Elementary Statistics: Picturing the World. (5th Ed.) Pearson Education Inc. 501 Boylston Street, Suite 900, Boston, MA 02116.
Statistics Unit 9
Page 581-584 #4, 5, 7, 15, and 18
4.) Describe the hypotheses for a two way ANOVA test.
Two way ANOVA Test will have three null hypotheses. One hypothesis will represent the independent variable, and its effects on the second hypothesis which is the dependent variable (main effect). The third null hypothesis is the interaction effect on both independent variables on the dependent variable.
5.) The table shows the cost per ounce (in dollars) for a random sample of toothpastes exhibiting very good stain removal, good stain removal, and fair stain removal. At a = 0.05, can you conclude that the mean costs per ounce are different? …show more content…
a.) Hₒ: μ¹ = μ² = μᶟ Hₐ: Claim- one mean is seen as being different from the others.
b.) Fₒ = 3.37 Rejection Region F > 3.37 c.) 1.02 d.) Fail to reject the Hₒ
e.) Evidence is not enough at 5% significance level to determine if the mean cost per ounce is different.
7.) The table shows the salaries (in thousands of dollars) of randomly selected individuals from the federal, state, and local levels of government. At a = 0.01, can you conclude that at least one mean salary is different? a.) Hₒ: μ¹ = μ² = μᶟ Hₐ: Claim- one mean is different from the others b.) Fₒ = 5.49 Rejection Region F > 5.49 c.) 22.99 d.) Reject Hₒ
e.) There is evidence at 1% significance level to determine that at least one mean salary is different.
15.) Table shows the number of female students who played on a sports team in grades 9 through 12 for a random sample of 8 high schools in a state. At a 0.01, can you reject the claim that the mean numbers of female students who played on a sports team are equal for all grades?
Analysis of Variance:
Column
Means
Column n Mean Standard Error
Grade 9 8 84.375 9.531784
Grade 10 8 79.25 9.090321
Grade 11 8 76.625 7.648383
Grade 12 8 70.75 6.9224014
ANOVA Table
Source df ss ms
Treatments 3 771.25 257.08334
Error 28 1574.75 559.8125
Total 31 16446
F-Stat P-Value
0.45923114 0.7129
P = 0.7129 > 0.01 It failed to reject Hₒ. Not enough evidence at 1% significance level that rejects the claim. Female student mean numbers are the same in every grade.
18.) The owner of a car dealership wants to determine if the gender of sales person and the type of vehicle sold affect the number of vehicles sold in a month. The block design shows the number of vehicles, listed by type, sold in a month by a random sample of eight sales people.
Reject the null hypothesis. The number of sales by a gender does have an effect on the sales of vehicles sold. There is a significance level of evidence to support the rejection. Reference
Larson, Ron and Farber, Betsy. (2012.). Elementary Statistics: Picturing the World. (5th Ed.) Pearson Education Inc. 501 Boylston Street, Suite 900, Boston, MA 02116.