Expected frequencies in the table above. If the frequencies are close to each ot

Question

Expected frequencies in the table above. If the frequencies are close to each other then we we can conclude that the digits were really random. Follow the following steps What statistical test can be used here? Determine if the conditions of the test are satisfied What is the degrees of freedom? Find the critical value from a table using the degrees of freedom. Make a decision as whether to reject the null hypothesis or not. Interpret this decision in the context of the problem. Are your friend's 100 random digits really random? An urban economist wants to determine whether the region of the US a resident lives in is associated with their general level of satisfaction with life. She randomly selects 100 residents 18 years of age or older from four geographic regions of the US: East, South, Midwest and West, a total of 400 US adults. She asks: "Are you generally satisfied or dissatisfied with the way things are going in your life at this time?" She summarizes the results in the following table. Perform a Test of Independence to determine whether geographic region a resident lives in and their level of satisfaction with their life are associated. Follow the steps:

Explanation / Answer

i. Ho: The level of satisfaction is independent of geographic regions where a resident lives

H1: The level of satisfaction is dependent of geographic regions where a resident lives.

ii. The chi-square test of independence of attributes -the statistical test to be used here.

iii.

Chi-square statistic = 0.45+0.00+0.64+0.02+0.57+0.00+0.82+0.02 = 2.52

(iv) Degree of freedom = (r-1)*(c-1) = (1)*(3) = 3

(v) The chi-square critical value at alpha 0.05 (two-tailed) is 9.3484.

(vi) As critical value is greater than statistic value , hence we fail to reject the null hypothesis.

(vii) The level of satisfaction is independent of geographic regions where a resident lives indicates that the data were collected randomly.

Observed Frequency US Regions Satisfaction Level East South Midwest West Total Satisfied 51 56 62 55 224 Dissatisfied 49 44 38 45 176 Total 100 100 100 100 400

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