A study was conducted to compare the proportion of single women getting more tha

Question

A study was conducted to compare the proportion of single women getting more than 8 hours of sleep to the proportion of married women getting more than 8 hours of sleep. Of 1000 single women, 420 reported that they sleep more than 8 hours on a regular basis. Of 1000 married women, 570 reported that they sleep more than 8 hours on a regular basis. Construct a 95% confidence interval for the difference of proportions between single and married women sleeping more than 8 hours on a regular basis. a. p1-p2= b.margin of error= c.lower and upper limit d. we are ___% confident that the true difference in population proportions is between ___ and ___

Explanation / Answer

p1 = 420/1000 = 0.42

p2 = 570/1000 = 0.57

The pooled sample proportion (P) = (p1 * n1 + p2 * n2)/(n1 + n2)

                                                      = (0.42 * 1000 + 0.57 * 1000)/(1000 + 1000)

                                                      = 0.495

SE = sqrt(P * (1 - P) * (1/n1 + 1/n2))

      = sqrt(0.495 * (1 - 0.495) * (1/1000 + 1/1000))

      = 0.022

At 95% confidence interval the critical value is z0.025 = 1.96

The 95% confidence interval is

p1 - p2 +/- z0.025 * SE

= (0.42 - 0.57) +/- 1.96 * 0.022

= -0.15 +/- 0.043

= -0.193, -0.107

The lower limit is -0.193

The upper limit is -0.107

We are 95% confident that the true difference in population proportions is between -0.193 and -0.107.

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