Question

Urban traffic congestion throughout the world has been increasing in recent​ years, especially in developing countries. The accompanying table shows the number of minutes that randomly selected drivers spend stuck in traffic in various cities on both weekdays and weekends. Complete parts a through e below.

	City_A	City_B	City_C	City_D
Weekday	90	42	55	54
	79	110	78	68
	132	62	78	42
	72	77	96	48
	97	95	122	53
Weekend	79	83	33	34
	91	24	85	44
	71	106	74	47
	72	76	62	43
	63	79	36	43

a) Using alpha = 0.05​, is there significant interaction between the city and time of the​ week?

Identify the hypotheses for the interaction between the city and time of the week. Choose the correct answer below.

A. H0​: City and time of the week do not​ interact, H1​: City and time of the week do interact

B. H0​: μCity ≠ μTime​, H1​: City=μTime

C. H0​: μCity=μTime​, H1​: μCity≠μTime

D. H0​: City and time of the week do​ interact, H1​: City and time of the week do not interact

Find the​ p-value for the interaction between city and time of the week.

​p-value=????

​(Round to three decimal places as​ needed.)

Draw the appropriate conclusion for the interaction between the city and time of the week. Choose the correct answer below.

A. Do not reject the null hypothesis. There is insufficient evidence to conclude that the city and time of the week interact.

B. Do not reject the null hypothesis. There is insufficient evidence to conclude that the means differ.

C. Reject the null hypothesis. There is insufficient evidence to conclude that the means differ.

D. Reject the null hypothesis. There is sufficientevidence to conclude that the city and time of the week interact.

​b) Using​ two-way ANOVA and α​=0.05​,does the city have an effect on the amount of time stuck in​ traffic?

Identify the hypotheses to test for the effect of the city. Choose the correct answer below.

A. H0​: μCity A=μCity B=μCity C=μCity D​, H1​: Not all city means are equal

B. H0​: μCity=μTime​, H1​: μCity≠μTime

C. H0​: μCity A≠μCity B≠μCity C≠μCity D​, H1​: μCity A=μCity B=μCity C=μCity D

D. H0​: μCity A=μCity B=μCity C=μCity D​, H1​: μCity A>μCity B>μCity C>μCity D

Find the​ p-value for the effect of the city.

​p-value=???

​(Round to three decimal places as​ needed.)

Draw the appropriate conclusion for the effect of the city. Choose the correct answer below.

A. Reject the null hypothesis. There is sufficient evidence to conclude that not all city means are equal.

B. Do not rejectthe null hypothesis. There is sufficient evidence to conclude that the means differ.

C. Do not rejectthe null hypothesis. There is insufficient evidence to conclude that not all city means are equal.

D. It is inappropriate to analyze because the city and the time of the week interact.

​c) Using​ two-way ANOVA and α​=0.05​, does the time of the week have an effect on the amount of time stuck in​ traffic?

Identify the hypotheses to test for the effect of the time of the week. Choose the correct answer below.

A.H0​: μWeekday=μWeekend​, H1​: Not all time of the week means are equal

B. H0​: μCity=μTime​, H1​:μCity≠μTime

C. H0​: μCity A=μCity B=μCity C=μCity D​, H1​: Not all time of the week means are equal

D. H0​: μWeekday≠μWeekend​, H1​:μWeekday=μWeekend

Find the​ p-value for the effect of the time of the week.

​p-value=???

​(Round to three decimal places as​ needed.)

Draw the appropriate conclusion for the effect of the time of the week. Choose the correct answer below.

A. Do not reject the null hypothesis. There is insufficient evidence to conclude that not all time of the week means are equal.

B. Do not reject the null hypothesis. There is sufficient evidence to conclude that the means differ.

C. Reject the null hypothesis. There is sufficient evidence to conclude that not all time of the week means are equal.

D. It is inappropriate to analyze because the city and the time of the week interact.

​

d) Are the means for weekdays and weekends significantly​ different?

A. Yes​,because there is insufficient evidence to conclude that not all time of the week means are equal.

B. No​, because there is insufficient evidence to conclude that not all time of the week means are equal.

C.Yes​, because there is sufficient evidence to conclude that not all time of the week means are equal.

D. The comparison is unwarranted because the city and the time of the week interact.

  

Answer 1

excel: data-data analyis: 2 way ANOVA with replication

Source of Variation	SS	df	MS	F	P-value
Sample	2325.625	1	2325.625	5.24957	0.028683
Columns	7476.275	3	2492.092	5.62533	0.003258
Interaction	814.075	3	271.3583	0.61253	0.611851
Within	14176.4	32	443.0125
Total	24792.38	39

a)

A. H0​: City and time of the week do not​ interact, H1​: City and time of the week do interact

p value =0.612

A. Do not reject the null hypothesis. There is insufficient evidence to conclude that the city and time of the week interact.

b)

A. H0​: μCity A=μCity B=μCity C=μCity D​, H1​: Not all city means are equal

p value =0.003

A. Reject the null hypothesis. There is sufficient evidence to conclude that not all city means are equal.

c)

A.H0​: μWeekday=μWeekend​, H1​: Not all time of the week means are equal

p value =0.029

C. Reject the null hypothesis. There is sufficient evidence to conclude that not all time of the week means are equal.

d)

C.Yes​, because there is sufficient evidence to conclude that not all time of the week means are equal.