Question

In a poll, 412 of 1030 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 (d) 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.

(B) Are the requirements for construction a confidence interval about p satisfied?

-a) Yes, the requirements are satisfied.

-b) No, the requirements of the sample being a random sample are not satisfied.

-c) No, the requirement that np(1-p) is greater than 10 is not satisfied.

-d) No, the requirement that the sample size is no more than 5% of the population is not satisfied.

C) Construct a 90% confidence interval for the proportion of adults aged 18 or older who believe there is too little spending on national defense.

The 90% confidence interval is ( ___ , ___ )

D) Is it possible that more than 45% of adults aged 18 or older believe there is too little spending on national defense? Is it likely?

-a) It is possible, but not likely.

-b) It is not possible.

-c) It is possible and likely.

Answer 1

A)point estimate for the proportion = = x/n = 412/1030 = 0.4

Point estimate is 0.4

B)Are the requirements for construction a confidence interval about p satisfied?

Yes.

C)Our aim is to construct 90% confidence interval.

= 1- c = 1- 0.90 = 0.10

= 1.645     (use z table)

Now , the margin of error is given by

E = /2 *  

= 1.645 * [(0.4 * (1 - 0.4)/1030]

=  0.0251

Now the confidence interval is given by

( - E)   ( + E)

(0.4 - 0.0251)   (0.4 - 0.0251 )

0.3748 0.4251  

90% confidence Interval is (0.3748 , 0.4251 )

D) Is it possible that more than 45% of adults aged 18 or older believe there is too little spending on national defense? Is it likely?

It is possible, but not likely.

(Because value 0.45 is not in our 90% interval)