Sample surveys on sensitive issues can give different results depending on how t

Question

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; 21% said they had used cocaine. Another 800 people were asked the question in a one-on-one personal interview; 26% said "yes." The remaining 800 were allowed to make an anonymous written response; 28% said "yes."

(a) Make a two-way table of answers (yes or no) by survey method.

(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, and all expected counts are greater than 5.0.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.    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.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.

What null and alternate hypotheses does 2 test?

H0: all proportions are equal
Ha: some proportions are differentH0: some proportions are equal
Ha: some proportions are different    H0: some proportions are different
Ha: some proportions are equalH0: all proportions are different
Ha: some proportions are equal

What are the degrees of freedom for this test?
df =  

(c) Compute the chi-squared component for each cell and give 2. Use this table or software to obtain the P-value of the test. (Round your answer to two decimal places.)
2 =  

P-value:

0.0005 < P < 0.00100.0010 < P < 0.0025    0.0025 < P < 0.0050.005 < P < 0.0100.010 < P < 0.020

(d) What do you conclude from these data?

There is significant evidence that the contact method makes a difference in response.There is not sufficient evidence to conclude that the contact method makes a difference in response

Yes No Phone One-on-one Anonymous

Explanation / Answer

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

H0: all proportions are equal
Ha: some proportions are different

degrees of freedom=2

c)

2 = 11.0933

P-value:  0.0025 < P < 0.0050.

d)There is significant evidence that the contact method makes a difference in response

Observed O yes No Total phone 168 632 800 one on one 208 592 800 Anonymous 224 576 800 Total 600 1800 2400 Expected E=rowtotal*column total/grand total yes No Total phone 200.000 600.000 800 one on one 200.000 600.000 800 Anonymous 200.000 600.000 800 Total 600 1800 2400 chi square =(O-E)^2/E yes No Total phone 5.120 1.7067 6.827 one on one 0.320 0.107 0.427 Anonymous 2.880 0.960 3.840 Total 8.320 2.773 11.0933

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