Question

Part 1:

In July 2019, Pew Research reported an interesting finding from a survey it conducted of 1,284 U.S. military veterans: 57 percent of U.S. veterans approve of Trump’s conduct as commander-in-chief of the U.S. armed forces. The survey employed probabilistic sampling.

Construct a 98 percent confidence interval for the true proportion of American veterans that approves of Trump’s conduct as commander-in-chief.

Group of answer choices

(a) (0.54, 0.60)

(b) (0.56, 0.58)

(c) (0.53, 0.61)

Part 2:

In the same survey effort referenced in Problem 5, Pew found that 41 percent of U.S. adults approve of Trump’s conduct as commander-in-chief. The sample size for this was 1,087 U.S. adults.

(a)The success-failure conditions are met here. Carry out a hypothesis test to see if the data at hand provide good evidence that a minority of U.S. adults approve of Trump’s performance as commander-in-chief. Report the test statistic and the p-value.

(b)How would we interpret the p-value?

(c)The success-failure conditions are met here. So, now let’s construct a 90 percent confidence interval for the proportion of Americans who approve of Trump’s conduct as commander-in-chief. Interpret the interval, and state whether the interval and the hypothesis test agree with each other.

Group of answer choices

(a) (0.245, 0.435); we are 90 percent confident the true proportion of US adults that approves of Trump’s conduct lies between 24.5 and 43.5 percent; the interval agrees with the test since the interval excludes 0.500.

(b) (0.385, 0.435); we are 90 percent confident the true proportion of US adults that approves of Trump’s conduct lies between 38.5 and 43.5 percent; the interval agrees with the test since the interval excludes 0.500.

(c) (0.385, 0.495); we are 90 percent confident the true proportion of US adults that approves of Trump’s conduct lies between 38.5 and 49.5 percent; the interval agrees with the test since the interval excludes 0.500.

Answer 1

Part 1

Assuming American veterans approves of Trump’s conduct as commander-in-chief, the confidence interval for the true proportion is given as -

where p = 57%

S.E. = sqrt(0.57 (1-0.57)/1284) = 0.0138 and z-value = 2.326

Thus, confidence interval is

Answer is a) (0.54, 0.60)

Part 2

a) Ho: p = 0.5

Ha: p < 0.5

S.E. = sqrt(0.5 (1-0.5)/1087) = 0.0152

Test statistic, z =

(0.41 - 0.5)/0.0152 = -5.93

p-value = P(z < -5.93) = 0.0000

b) As p-value is very small, we can easily reject the null hypothesis and conclude that the findings of Pew survey is correct.

c) Confidence interval is given as

(0.385, 0.435)