Question

Question 4 (1 point) You work at Happy Joe's family restaurant and want to see if customer meal satisfaction and gender are related to one another. You take a sample of customers and ask them if they were satisfied with their meal and note their gender. To test at the 0.05 level to determine if Satisfaction and Gender are dependent, calculate the chi-square test statistic and p-value. Cross Tabulation of Satisfaction vs. Gender Female Male Unhappy 55 22 Satisfied 15 Hapo 10 32 1) 40.761, the degrees of freedom is 6, and the p-value is 0.0000
4 cont

5cont

6cont

Answer 1

Question 4.

	Gender	Total
Male	Female
Satisfaction	Unhappy	55	22	77
Satisfied	62	15	77
Happy	10	32	42
Total	127	69	196

In this problem, the null & alternative hypothesis are:

Ho: Satisfaction and Gender are independent.

Ha: Satisfaction and Gender are not independent.

For this analysis, the significance level is 0.05. Using sample data, we will conduct a chi-square test for independence.

Applying the chi-square test for independence to sample data, we compute the degrees of freedom, the expected frequency counts, and the chi-square test statistic. Based on the chi-square statistic and the degrees of freedom, we determine the p-value.

df = (r - 1) * (c - 1) = (3 - 1) * (2 - 1) = 2, under H0

where, r = Number of rows, c = Number of columns

Er,c = (nr * nc) / n

nr = rth row total, nc = cth column total, Er,c = Expected value of the (r,c)th cell

E1,1 = (77 * 127) / 196 = 49.893
E1,2 = (77 * 69) / 196 = 27.107
E2,1 = (77 * 127) / 196 = 49.893
E2,2 = (77 * 69) / 196 = 27.107
E3,1 = (42 * 127) / 196 = 27.214
E3,2 = (42 * 69) / 196 = 14.786

  

6 _x? = [(Or,e – Er,e)?/Er.cI 2=1

$1591820538874_blob.png$ = (55 - 49.893)2 / 49.893 + ... + (32 - 14.786)2 / 14.786

= 0.523 +0.962 + 2.938 + 5.407 + 10.889 + 20.041 = 40.761

The p-value of the test statistic at 5% significance level with degrees of freedom 2 = 0.0000, which is less than $1591820538877_blob.png$ = 0.05.

Therefore, we can conclude that the p- value is significant at the significance level 0.05.

Hence, we can conclude that the variables Satisfaction and Gender are not independent. Thus, they are dependent i.e. Satisfaction is associated with Gender i.e. higher values in one variable results in higher or lower values of other variables.

So Correct option is: (5) 40.761, the degrees of freedom is 2, and the p-value is 0.0000.

Question 5.

	Response	Total
Worse	Same	Better
Party Affiliation	Independent	41	56	35	132
Republican	35	29	13	77
Democrat	9	24	8	41
Total	85	109	56	250

In this problem, the null & alternative hypothesis are:

Ho: Party Affiliation and Response are independent.

Ha: Party Affiliation and Response are not independent.

For this analysis, the significance level is 0.05. Using sample data, we will conduct a chi-square test for independence.

Applying the chi-square test for independence to sample data, we compute the degrees of freedom, the expected frequency counts, and the chi-square test statistic. Based on the chi-square statistic and the degrees of freedom, we determine the p-value.

df = (r - 1) * (c - 1) = (3 - 1) * (3 - 1) = 4, under H0

where, r = Number of rows, c = Number of columns

Er,c = (nr * nc) / n

nr = rth row total, nc = cth column total, Er,c = Expected value of the (r,c)th cell

E1,1 = (132 * 85) / 250 = 44.88
E1,2 = (132 * 109) / 250 = 57.552
E1,3 = (132 * 56) / 250 = 29.568
E2,1 = (77 * 85) / 250 = 26.18
E2,2 = (77 * 109) / 250 = 33.572
E2,3 = (77 * 56) / 250 = 17.248

E3,1 = (41 * 85) / 250 = 13.94
E3,2 = (41 * 109) / 250 = 17.876
E3,3 = (41 * 56) / 250 = 9.184

  

6 _x? = [(Or,e – Er,e)?/Er.cI 2=1

$1591820538874_blob.png$ = (41 - 44.88)2 / 44.88 + ... + (8 - 9.184)2 / 9.184

= 0.335 + 0.042 + 0.998 + 2.971 + 0.623 + 1.046 + 1.751 + 2.098 + 0.153 = 10.017

The p-value of the test statistic at 5% significance level with degrees of freedom 4 = .040142, which is less than $1591820538877_blob.png$ = 0.05.

Therefore, we can conclude that the p- value is significant at the significance level 0.05.

Hence, we can conclude that the variables Party Affiliation and Response are not independent. Thus, they are dependent i.e. Party Affiliation is associated with Response i.e. higher values in one variable results in higher or lower values of other variables.

So Correct option is: (1) We decide that Party Affiliation and Response are related to one another based on a p-value = 0.0401

Question 6.

	Gender	Total
Male	Female	Unknown
Satisfaction	Unhappy	29	30	49	108
Satisfied	8	15	31	54
Happy	23	16	12	51
Total	60	61	92	213

In this problem, the null & alternative hypothesis are:

Ho: Satisfaction and Gender are independent.

Ha: Satisfaction and Gender are not independent.

For this analysis, the significance level is 0.1. Using sample data, we will conduct a chi-square test for independence.

Applying the chi-square test for independence to sample data, we compute the degrees of freedom, the expected frequency counts, and the chi-square test statistic. Based on the chi-square statistic and the degrees of freedom, we determine the p-value.

df = (r - 1) * (c - 1) = (3 - 1) * (3 - 1) = 4, under H0

where, r = Number of rows, c = Number of columns

Er,c = (nr * nc) / n

nr = rth row total, nc = cth column total, Er,c = Expected value of the (r,c)th cell

E1,1 = (108 * 60) / 213 = 30.423
E1,2 = (108* 61) / 213 = 30.93
E1,3 = (108 * 92) / 213 = 46.648

E2,1 = (54* 60) / 213 = 15.211
E2,2 = (54 * 61) / 213 = 15.465
E2,3 = (54 * 92) / 213 = 23.324

E3,1 = (51 * 60) / 213 = 14.366
E3,2 = (51 * 61) / 213 = 14.606
E3,3 = (51 * 92) / 213 = 22.028

  

6 _x? = [(Or,e – Er,e)?/Er.cI 2=1

$1591820538874_blob.png$ = (29 - 30.423)2 / 30.423 + ... + (12 - 22.028)2 / 22.028

= 0.067 + 0.028+ 0.119 + 3.418 + 0.014 + 2.526 + 5.189 + 0.133 + 4.565 = 16.059

The p-value of the test statistic at 10% significance level with degrees of freedom 4 = .002941, which is less than $1591820538877_blob.png$ = 0.10.

Therefore, we can conclude that the p- value is significant at the significance level 0.10

Hence, we can conclude that the variables Satisfaction and Gender are not independent. Thus, they are dependent i.e. Satisfaction is associated with Gender i.e. higher values in one variable results in higher or lower values of other variables.

So Correct option is: (4) We find that Satisfaction and Gender are related to each other, based on a p-value of 0.0029