Income By State A student at a private college in New England wants to see if th
ID: 3062692 • Letter: I
Question
Income By State
A student at a private college in New England wants to see if there is a difference in mean household incomes for students from the various New England states. The table below gives the sample sizes and means from her study and the results of an ANOVA test run on the data. She wants to test for a difference in mean household income for all students from the different states.
ANOVA Results:
F = 2.798
P-value = 0.0339
Please respond to the following questions, using the table above.
For your answer, make sure you show and explain your work.
1. Using the information above to respond the following questions at the 0.10 level of significance. Note that there is no claim, but that does not affect the hypotheses.
a. What is the null hypothesis and alternative hypothesis? Be specific - don't use generic wording.
b. Make a decision about whether or not to reject the null by comparing the p-value to the alpha level.
c. Make a concluding statement based on the results. Be specific: Is there sufficient evidence to conclude that there is a difference in mean family income for all students from the different states?
d. Does your conclusion change at the 0.05 level of significance? at the 0.01 level of significance?
2. Using the information above to respond the following questions at the 0.05 level of significance. Note that there is no claim, but that does not affect the hypotheses.
a. What is the null hypothesis and alternative hypothesis? Be specific - don't use generic wording.
b. Make a decision about whether or not to reject the null by comparing the p-value to the alpha level.
c. Make a concluding statement based on the results. Be specific: Is there sufficient evidence to conclude that there is a difference in mean family income for all students from the different states?
d. Does your conclusion change at the 0.10 level of significance? at the 0.01 level of significance?
3. Using the information above to respond the following questions at the 0.01 level of significance. Note that there is no claim, but that does not affect the hypotheses.
a. What is the null hypothesis and alternative hypothesis? Be specific - don't use generic wording.
b. Make a decision about whether or not to reject the null by comparing the p-value to the alpha level.
c. Make a concluding statement based on the results. Be specific: Is there sufficient evidence to conclude that there is a difference in mean family income for all students from the different states?
d. Does your conclusion change at the 0.10 level of significance? at the 0.05 level of significance?
Student's State Sample Size Mean Household Income New Hampshire 11 $97,607 Connecticut 14 $96,224 Massachusetts 19 $85,790 Vermont 13 $77,903 Maine 7 $77,471Explanation / Answer
1)
a) The null hypothesis is The household prices for all students at all states are significant
b) From the informatio given we can say that F calculated > F tabulated ( 0.14) hence we can come to a conclusion that the null hypothesis is rejected and the househol proces for all students at all states are not insignificant
2)
keeping the level of significance at 0.05 from 0.1 we would like to check the significancy of the data hence ,
a) The null hypothesis is The household prices for all students at all states are significant
b) From the informatio given we can say that F calculated > F tabulated ( 0.18) hence we can come to a conclusion that the null hypothesis is rejected and the househol proces for all students at all states are not insignificant
c) There are sufficient evidence to conclude that there is a difference in mean family income for all students from the different states. Both at 0.1 & 0.05 los we didn't changed the hypothesis yet got the same result at F calculated is always way greater than F tabulated at different los.
d) No, the conclusion does not change at both 0.1 & 0.01 los.