In a poll 204 of 1020 randomly selected adults aged 18 or ol

In a poll, 204 of 1020 randomly selected adults aged 18 or older stated that they believe there is too little spending on national defense. Use this information to complete parts (a) through (e) below. (a) Obtain a point estimate for the proportion of adults aged 18 or older who feel there is too little spending on national defense. p = (b) Verify that the requirements for constructing a confidence interval about p are satisfied. Are the requirements for constructing a confidence interval about p satisfied? (c) Construct a 99% confidence interval for the proportion of adults aged 18 or older who believe there is too little spending on national defense. The 99% confidence interval is (d) Is it possible that more than 25% of adults aged 18 or older believe there is too little spending on national defense? Is it likely? (e) Use the results of part (c) to construct a 99% confidence interval for the population proportion of adults aged 18 or older who do not believe there is too little spending on national defense.

Solution

(a)

Point estimate , p = 204/1020 = 0.2 Answer

(b)

A . Yes , the requirements for contructing a confidence interval are satisfied.

(c)

For, 99% confidence interval ,

Margin of error E = z_alpha/2 * sqrt(pq/n) = 2.575 * sqrt ((0.2*0.8) / 1020) = 0.032

Therefore , confidence interval

= ( 0.2-0.032 , 0.2+0.032)

= (0.168 , 0.232) Answer

(d)

A. It is not possible since 25% is out of the confidence interval ( 16.8% , 23.2%).

(e)

CI = ( 0.8-0.032 , 0.8 + 0.032) = (0.768 , 0.832) Answer