My Notes Ask Your Sample surveys on sensitive issues can give different results

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My Notes Ask Your Sample surveys on sensitive issues can give different results depending on how the question is asked. A study divided 2400 respondents into 3 groups at random. All were asked if they had ever used cocaine. One group of 800 was interviewed by phone; 22% said they had used cocaine. Another 800 people were asked the question in a one-on-one personal interview; 27% said "yes." The remaining 800 were allowed to make an anonymous written response; 29% said "yes. (a) Make a two-way table of answers (yes or no) by survey method Yes No Phone One-on-one Anonymous (b) Can we safely use the chi-squared test? Yes, we can safely use the chi-squared test because the study randomly assigns the subjects to the interview types, although more than 20% of the expected counts are smaller than 5.0. O No, we can not safely use the chi-squared test because the study does not randomly assign the subjects to the interview types, although all expected counts are greater than 5.0. O No, we can not safely use the chi-squared test because the study did not randomly assign the subjects to the interview types, and more than 20% of the expected counts are smaller than 5.0. o Yes, we can safely use the chi-squared test because the study randomly assigns the subjects to the interview types, and all expected counts are greater than 5.0. What null and alternate hypotheses does X test? O Ho: some proportions are equal Ha: some proportions are different Ho: some proportions are different Ha: some proportions are equal Ho: all proportions are equal Ha: some proportions are different Ho: all proportions are different Ha: some proportions are equal What are the degrees of freedom for this test? (c) Compute the chi-squared component for each cell and giveX2. Use this table or software to obtain the p value of the test. (Round your answer to two decimal places.) P-value 0.0005 P 0.0010 0.0010 0025

Explanation / Answer

We have given,

800 interviewed on phone, where 22% of 800 = 176 said Yes then remaining 800 - 224 = 576 are not using cocaine

800 interviewed on one to one, where 27% of 800 = 216 said Yes then remaining 800 - 216 = 584 are not using cocaine

800 interviewed anonymously, where 29% of 800 = 232 said Yes then remaining 800 - 232 = 568 are not using cocain

a) Create table

We can construct below table by calculating expected frequencies (E),

All bracket values are expected frequencies which are calculated by using below formula

E = (Row total x Column total) / Overall total = (RT x CT) / N where N = 2400

For example,

E11 = (800 x 624) / 2400 = 208

b) Can we safely use chisquare test?

Yes, we can safely use chisquare test because the study randomly assigns the subjects to the interview types and all expected counts are greater than 5.0

c) What null and alternative hypothesis does chisquare test?

H0: All proportions are equal

Ha: Some proportions are different

Degrees of freedom = (R-1) x (C-1) = (3-1) x (2-1) = 2 x 1 = 2

Where R: number of rows = 3, and C: number of columns = 2

c) Compute chisquare components for each cell

Let us construct another table where we represent all observed frequencies(O) and all Expected frequencies(E) in order to calculate chisquare test

Chi-square = sum((O-E)^2/E) = 10.8108

P-Value = p(chisquare > 10.8108) = CHIDIST(10.8108,2) = 0.0045

P-value lies between 0.0025 < p < 0.005

d) Conclusion:

Since p value is small, we reject the null hypothesis and conclude that There is significant evidence that the contact method makes a difference in respose

Yes No Phone 176 624 One on One 216 584 Anonymous 232 568

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