Question : The roads in a particular state are in very poor condition, but the state claims : 2146835

The roads in a particular state are in very poor condition, but the state claims that it does not have enough money to repair the roads. A proposal is on the ballot to raise the sales tax in the state from 6% to 7% to pay for repairing the roads. A month before the election, a survey of likely voters is taken. A random sample of 500 likely voters under the age of 30 is selected, a random sample of 500 likely voters aged 30-49 is selected, and a random sample of 500 likely voters aged 50 or more is selected. Each likely voter is asked whether he/she is in favor of the increase in the sales tax or not.

48) Choose the correct hypotheses to test whether there is an association between the response to whether to increase the sales tax or not and age.

A) H₀: Among likely voters, opinions on the sales tax increase and age are associated

H_a: Among likely voters, opinions on the sales tax increase and age are independent

B) H₀: There is no difference in the proportions of likely voters who favor and who do not favor the increase in sales tax

H_a: There is a difference in the proportions of likely voters who favor and who do not favor the increase in sales tax

C) H₀: There is a difference in the proportions of likely voters who favor and who do not favor the increase in sales tax

H_a: There is no difference in the proportions of likely voters who favor and who do not favor the increase in sales tax

D) H₀: Among likely voters, opinions on the sales tax increase and age are independent

H_a: Among likely voters, opinions on the sales tax increase and age are associated

Solve the problem.

49) Recently, many states have been considering legalizing the use of marijuana. A survey was taken last year where adults in one state were asked if they favored legalizing the use of marijuana. The following table displays the percentage of adults in the state who favor and who do not favor the legalization of marijuana for both males and females:

	Male	Female
Favor legalizing marijuana	38.60%	35.50%
Do not favor legalizing marijuana	61.40%	64.50%

Choose the reason(s) why you cannot perform a chi-square test on the data.

I. The percentages do not add up to 100%.

II. There is not enough information to convert the percentages to counts.

III. The samples were not randomly selected

A) III only

B) I only

C) I, II, and III

D) II only

50) Recently, many states have been considering legalizing the use of marijuana. A survey was taken last year where adults in one state were asked if they favored legalizing the use of marijuana. The following table displays the percentage of adults in the state who favor and who do not favor the legalization of marijuana for both males and females:

	Male	Female
Favor legalizing marijuana	38.60%	35.50%
Do not favor legalizing marijuana	61.40%	64.50%

What additional information would be necessary to be able to perform a chi-square test on the data.

A) None of these

B) We would have to know the total number of those favoring legalizing marijuana in the sample and the total number of those not favoring legalizing marijuana in the sample.

C) We would just need to know the total number of people in the sample.

D) We would have to know the total number of men in the sample and the total number of women in the sample.

51) The American Academy of Pediatrics recommends breast milk as the best nutrition for infants. A survey was conducted to see if pregnant women in their last trimester of pregnancy planned to breast feed their babies. It was thought that the income level of the women might be related to whether they planned to breast feed or not. The table below shows the results of the study:

 

Income level	Plan to breast feed	Do not plan to breast feed
Low	28	27
Middle	38	26
Hight	29	14

x2 – Test X2 = 2.743182 P = 0.253703 Df=2

 

Assume that all conditions for testing have been met. This was an observational study of randomly selected pregnant women in their last trimester of pregnancy. Test whether there is an association between whether a woman plans to breast feed her baby or not and her income level, using a significance level of 0.05. Choose the correct decision and conclusion regarding the null hypothesis that no association exists. Refer to the computer output above.

A) Fail to reject the null hypothesis; income level and plan to breast feed are not associated.

B) Reject the null hypothesis; income level and plan to breast feed are associated.

C) Fail to reject the null hypothesis; income level and plan to breast feed are associated.

D) Reject the null hypothesis; income level and plan to breast feed are not associated.

52) A study of middle school and high school students was conducted to examine the ethnic/racial self-classification of adolescents. A group of 500 students in the eighth grade were randomly selected and followed for 4 years. At the beginning of each year, the students were asked among many questions to classify themselves as White, Black, Hispanic, or Multiracial (additional classifications were eliminated because of small frequencies). At the end of the study, the number of times each student changed his/her classification was recorded. The table below shows the results from the study.

	Number of changes
Racial Classification in 8th grade	0	1	2+
White	402	25	17
Black	44	12	6
Hispanic	83	17	10
Multiracial	111	36	42

x2 – Test X2 = 94.208413 P = 0.000000 Df=6

 

Test the hypothesis that the number of changes in racial classification is associated with students' racial classification in eighth grade, using a significance level of 0.05. Choose the correct decision regarding the null hypothesis and decision. Refer to the computer output above.

A) Fail to reject the null hypothesis; racial classification in 8th grade is associated with number of changes in racial classification

B) Fail to reject the null hypothesis; racial classification in 8th grade is not associated with number of changes in racial classification

C) Reject the null hypothesis; racial classification in 8th grade is not associated with number of changes in racial classification

D) Reject the null hypothesis; racial classification in 8th grade is associated with number of changes in racial classification

x2 – Test X2 = 2.941951 P = 0.229710 Df=2

53) Suppose a study was conducted to see whether there is an association between marital status and vehicle color. The table below shows the results from the study. Assume all conditions for testing have been met.

	Vehicle clolor
	Red	Black/white/silver	Blue/green/ther
Married	28	27	19
Unmarried	29	14	18

 

This was an observational study of randomly chosen vehicle owners. Test the hypothesis that marital status and vehicle color are associated, using a significance of 0.05. Choose the correct decision regarding the null hypothesis and conclusions. Refer to the computer output above.

A) Reject the null hypothesis; marital status and vehicle color are associated.

B) Fail to reject the null hypothesis; marital status and vehicle color are not associated.

C) Reject the null hypothesis; marital status and vehicle color are not associated.

D) Fail to reject the null hypothesis; marital status and vehicle color are associated.

x2 – Test X2 = 8.25774 P = 0.08258 Df=4

54) A study was conducted to see if teenagers work longer hours to pay for newer cars. A random sample of teenagers was taken and the number of hours each worked was recorded along with the age of the car that each usually drove. The table below shows the results from the study.

	Age of car usually driven
Hours worked per week	Less than 4	04-Aug	Over 8
Under 15	7	8	14
15 - 25	36	17	16
Over 25	28	17	17

 

Test the hypothesis that the age of the car driven is associated with the number of hours worked per week, using a significance level of 0.10. Choose the correct decision regarding the null hypothesis and decision. Refer to the computer output above.

A) Fail to reject the null hypothesis; age of car usually driven is associated with number of hours worked per week

B) Fail to reject the null hypothesis; age of car usually driven is not associated with number of hours worked per week

C) Reject the null hypothesis; age of car usually driven is associated with number of hours worked per week

D) Reject the null hypothesis; age of car usually driven is not associated with number of hours worked per week

55) Choose the statement that is not true about the chi-square test or state that none of the statements is true.

A) The conclusion of a chi-square test tells us whether the variables are associated as well as how they are associated.

B) To conduct a chi-square test you must have a large enough sample. This condition is met if each of the observed cells is 5 or more.

C) None of these statements are true.

D) To conduct a chi-square test you must have a large enough sample. This condition is met if the sample size is at least 40.

56) Choose the statement that is not true about the chi-square test or state that all the statements are true.

A) The test statistic is the same for a test of homogeneity or a test for independence, it is chi-square (χ²).

B) All of these statements are true.

C) The conclusion of a chi-square test tells whether the variables under study are associated and how they are associated.

D) To conduct a chi-square test you must have a large enough sample. This condition is met if each expected value is 5 or more.

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

57) Suppose a random sample of 1,105 adults were asked about their opinion regarding salaries of full-time employees at a local state funded university. Respondents were asked whether salaries at the university were (a) too low, (b) adequate, or (c) too high. Respondents were also classified by income level. State the correct hypothesis to test whether there is an association between the response to the questions and income level.