Question

The authors of the article “Accommodating Persons with AIDS: Acceptance and Rejection in Rental Situations” (Journal of Applied Social Psychology [1999]: 261-270) stated that, even though landlords participating in a telephone survey indicated that they would generally be willing to rent to persons with AIDS, they wondered whether this was true in practice. To investigate, the researches independently selected two random samples of 80 advertisements for rooms for rent from newspapers advertisements in three large cities. An adult male caller responded to each ad in the first sample of 80 and inquired about the availability of the room and was told that the room was still available in 61 of these calls. The same caller also responded to each ad in the second sample. In these calls, the caller indicated that he was currently receiving some treatment for AIDS and was about to be released from the hospital and would require a place to live. The caller was told that a room was available in 32 of these calls. Based on this information, the authors concluded that “reference to AIDS substantially decreased the likelihood of a room being described as available”. Do the data support this conclusion? (Use ? = 0.01)

Answer 1

Sample size, n1 =80

Sample proportion, =x1/n1 =61/80 =0.7625

Sample size, n2 =80

Sample proportion, =x2/n2 =32/80 =0.40

Null Hypothesis(H0):

p2 p1 (or) p2 - p1 0 (The difference is not significantly less than 0).

Alternative Hypothesis(H1):

p2 < p1 (or) p2 - p1 < 0 (The difference is significantly less than 0). (left-tailed test).

(p1 =Population proportion of sample 1; p2 =Population proportion of sample 2).

Test statistic(Z):

Pooled sample proportion, =(x1+X2)/(n1+n2) =(61+32)/(80+80) =0.58125

Standard Error, SE = = =0.078006

Test statistic, Z = =(0.40 - 0.7625)/0.078006 = -4.65

Critical value(Z_critical):

At 0.01 significance level (​​​​​​), for a left-tailed test, the critical value of Z is: Z_critical = -2.33

Decision criteria:

If Z > Z_critical, reject H0. Otherwise do not reject H0. (consider absolute values only).

Conclusion:

Since the absolute value of test statistic(4.65) is greater than the absolute critical value(2.33), we reject the null hypothesis(H0) at 0.01 significance level in favor of the alternative hypothesis(H1) and conclude that we have sufficient evidence to claim that the difference between p2 and p1 is significantly less than 0.

Thus, the data supports the conclusion of the authors - "reference to AIDS substantially decreased the likelihood of a room being described as available".