Question

1.

A major food manufacturer is concerned that the sales for its skinny french fries have been decreasing. As a part of a feasibility study, the company conducts research into the types of fries sold across the country to determine if the type of fries sold is independent of the area of the country. The results of the study are shown in the table. Conduct a test of independence.

Type of Fries	Northeast	South	Central	West
skinny fries	70	50	20	25
curly fries	100	60	15	30
steak fries	20	40	10	10

a. Find the Test statistic

2.

Car manufacturers are interested in whether there is a relationship between the size of car an individual drives and the number of people in the driver’s family (that is, whether car size and family size are independent). To test this, suppose that 800 car owners were randomly surveyed with the results in the table. Conduct a test of independence.

Family Size	Sub & Compact	Mid-size	Full-size	Van & Truck
1	20	35	40	35
2	20	50	70	80
3–4	20	50	100	90
5+	20	30	70	70

a. Find the Test statistic

Answer 1

Answer Date: 10/11/2019 1) To test the hypothesis is that the type of fries sold is dependent of the area of the country at 5% significance level. The null and alternative hypothesis is, The null hypothesis is that the type of fries sold is independent of the area of the country. The alternative hypothesis is that the type of fries sold is dependent of the area of the country. The chi-square statistics is, By using Excel software, find chi-square test statistics with the help of following steps: 1) Import the data. 2) Select Contingency table from Chi-Square in MegaStat option from Add-Ins menu. Select Chi-Square and Expected frequencies in Output options. 4) Click Ok.

Chi-square Contingency Table Test for Independence South West 50 Central 20 16.500 25 55.000 23.833 Total 165 165.000 205 205.000 60 15 30 | Northeast 70 69.667 100 86.556 20 33.778 190 190.000 skinny frie Observed Expected curly fries Observed Expected steak frie: Observed Expected Total Observed Expected 80 68.333 40 26.667 150 150.000 20.500 10 8.000 45 45.000 29.611 10 11.556 65 65.000 80.000 450 450.000 18.837 chi-square 6 df .0044 p-value From the Excel output, the chi-square test statistic is 18.837|. The p-value is, From the Excel output, the p-value is 0.0044. The p-value is 0.0044

Decision The conclusion is that the significant p-value is less than 0.05 which is 0.0044, so the null hypothesis is rejected at 5% level of significance. There is sufficient evidence to indicate that the type of fries sold is dependent of the area of the country. The result is statistically significant 2) To test the hypothesis is that car size and family size are dependent at 5% significance level. The null and alternative hypothesis is, The null hypothesis is that car size and family size are independent. The alternative hypothesis is that car size and family size are dependent The chi-square statistics is,

By using Excel software, find chi-square test statistics with the help of following steps: 1) Import the data. 2) Select Contingency table from Chi-Square in MegaStat option from Add-Ins menu. Select Chi-Square and Expected frequencies in Output options. 4) Click Ok. 3) Chi-square Contingency Table Test for Independence 20 Full-size | Van & Truck | 40 45.500 44.688 35 Total 130 130.000 20 Mid-size 35 26.813 50 45.375 50 53.625 70 80 Sub & Compact Size 1 Observed Expected 13.000 Size 22 Observed Expected 22.000 Size 3-4 Observed 20 Expected 26.000 Size 5+ Observed 20 Expected 19.000 Total Observed Expected 80.000 220 30 77.000 100 91.000 70 66.500 280 280.000 75.625 | 220.000 90 260 89.375 260.000 190 65.313 | 190.000 275 800 275.000 800.000 70 80 39.188 165 165.000 15.828 chi-square 9 df .0706 p-value

From the Excel output, the chi-square test statistic is 15.828. The p-value is, From the Excel output, the p-value is 0.0706. The p-value is 0.0706 Decision The conclusion is that the significant p-value is higher than 0.05 which is 0.0706, so the null hypothesis is not rejected at 5% level of significance. There is insufficient evidence to indicate that car size and family size are dependent. The result is not statistically significant.