A survey of randomly selected university students found that 83 of the 110 first year students and 87 of the 120 second year students surveyed had purchased used textbooks in the past year.Construct a 98% confidence interval for the difference in the proportions of first and second year university students who purchased used textbooks.
A)(-0.084,0.868)
B)(-0.105,0.164)
C)(0.641,0.868)
D)(0.620,0.890)
E)(0.620,0.868)

Question

Quizplus · Accepted Answer

To construct a 98% confidence interval for the difference in proportions, we first calculate the sample proportions: $p_1 = \frac{83}{110}$ for first year students and $p_2 = \frac{87}{120}$ for second year students. Then, we use the formula for the confidence interval for two proportions, which includes the critical value for the desired confidence level (which for 98% confidence is approximately 2.33, using the Z-distribution), the sample proportions, and the sample sizes. The calculation involves finding the standard error of the difference in proportions and then applying the critical value to find the margin of error. The correct interval, given the calculations, is (-0.105, 0.164), which suggests that the true difference in proportions could range from -10.5% to 16.4%, indicating that there is no significant difference between the proportions of first and second year students who purchased used textbooks.

A Survey of Randomly Selected University Students Found That 83