Question

5.Calculate the standard error (se) for the following situations. a. 268 people said yes out of a sample of size 1049 SE = 0.0135 b. 717 people out of 1237 believe that the governor is doing a satisfactory job SE= 0.0140 6.For each part of the exercise 5, give a 95% confidence interval. Write the answer in a form similar to this: (45.73%, 59.14%).

Answer 1

Date: 09/01/2020 Answer Solution 5 a) The standard error is, First, compute the proportion then find the standard error. The proportion is, 268 1049 = 0.2555

The standard error is, P(1– ô) SE, 0.2555(1-0.2555) %3D 1049 = 0.0135 The standard error is 0.0135 b) The standard error is, First, compute the proportion then find the standard error.

The proportion is, 717 1237 = 0.5796 The standard error is, P(1- p) SE, . = 0.5796(1– 0.5796) 1237 = 0.0140 The standard error is 0.0140. Solution 6

A 95% confidence interval for the proportion of people say "yes" is, First, compute the z-critical value then find confidence interval. The z-critical value is, From the standard normal table, the z-critical value at 95% confidence is 1.96. 95% C.I. = ê ±zcx SE3 = 0.2555 +1.96x 0.0135 = 0.2291 to 0.2819 = 22.91% to 28.19% A 95% confidence interval for the proportion of people say "yes" is 22.91% to 28.19% A 95% confidence interval for the proportion of people say governor doing a good job is, First, compute the z-critical value then find confidence interval. The z-critical value is,

From the standard normal table, the z-critical value at 95% confidence is 1.96. 95% C.I. = p±zc× SE3 = 0.5796 ±1.96 x 0.0140 = 0.5521 to 0.6071 = 55.21% to 60.71% A 95% confidence interval for the proportion of people say governor doing a good job is 55.21% to 60.71%