A news article reports that \"Americans have differing views on two potentially
ID: 3228568 • Letter: A
Question
A news article reports that "Americans have differing views on two potentially inconvenient and invasive practices that airports could implement uncover potential terrorist attacks." This news piece was based on a survey conducted among a random sample of 1, 137 adults nationwide, interviewed by telephone November 7-10. 2010, where one of the questions on the survey was "Some airports are now using 'full-body' digital x-ray machines to electronically screen passengers in airport security lines. Do you think these new x-ray machines should or should not be used at airports?" Below is a summary of responses based on party affiliation. Conduct an appropriate hypothesis test evaluating whether there is a difference in the proportion Republicans and Democrats who think the full-body scans should be applied in of airports. Assume that all relevant conditions are met.Explanation / Answer
Testing of hypothesis for difference in proportion :
H0 = There is no significance difference in the population proportion of Republicans and Democrats who think the full body scans should be applied in airports. P1 = P2
H1 = There is significance difference in the population proportion of Republicans and Democrats who think the full body scans should be applied in airports. P1 P2
X1 = 264, n1 = 318, p1 = 264/318=0.8301
X2 =299, n2 = 369, p2 = 299/369=0.8102
Z = | p1 – p2 | / [pq(1/n1 + 1/n2)]
Where p = x1 + x2 / n1 + n2 = (264+299)/(318+369) = 0.8195
q = 1 - p = 0.1805
z = |0.8301-0.8102|/ [0.8195*0.1805*0.00585] = 0.0199/0.02941 = 0.6766
The table value of z at =0.05 for two tailed test is 1.96. Since ztab > zcal , we accept the null hypothesis. Hence we conclude that there is no significance difference in the population proportion of Republicans and Democrats who think the full body scans should be applied in airports.
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