Question

A survey of data base administrators is conducted. In a random sample of equation, n=150, x=63 of them were found to have over 10 years of experience. Construct 1-a=0.90 confidence interval for the population proportion p of data base administrators with over 10 years of experience.____________________________________________________________1) The sample proportion of data base administrators having over 10 years of experiences is closest toa.63 b.1.645 c.4.2 d.42 e.none of the above2) The half width of this confidence interval is closest to a.0.0033 b.0.0403 c.0.0663 d.0.0790 e.none of the above3) The left limit of this confidence interval L is closest to a.0.4990 b.0.4863 c.0.3537 d.0.3140 e.none of the above4) The right limit of this confidence interval R is closest to a.0.4990 b.0.4863 c.0.3537 d.0.3410 e.none of the above5) The conclusion is a.With 90% confidence, 0.3410 < p < 0.4863 b.With 90% confidence, 0.3537 < p < 0.4990 c.With 90% confidence, 0.3410 < p < 0.4990 d.With 90% confidence, 0.3537 < p < 0.4863 e.none of the above

Answer 1

Explanation:

Sample proportion is x/n

Where

p = probability of success

n = number of samples

p = x/n = 63/150 = 0.42

q = 1 - p = 1 - 0.42 = 0.58

To determine the z score, we subtract the confidence level from 100% to get α

Since 1 - α = 0.9

α = 1 - 0.9 = 0.1

α/2 = 0.1/2 = 0.05

This is the area in each tail. Since we want the area in the middle, it becomes

1 - 0.05 = 0.95

The z score corresponding to the area on the z table is 1.645. Thus, confidence level of 90% is 1.645

Confidence interval is written as

(Sample proportion ± margin of error)

Margin of error = z × √pq/n

= 1.645 × √(0.42 × 0.58)/150

= 0.066

The lower end of the confidence interval is

0.42 - 0.066 = 0.354

The upper end of the confidence interval is

0.42 + 0.066 = 0.486

Therefore, the answers to the given questions are

1) d. 0.42

2) the quantity after the ± is the half width. It is also the margin of error. Thus

The half width of this confidence interval is closest to

d. 0.0663

3) c.0.3537

4) b.0.4863

5) d.With 90% confidence, 0.3537 < p < 0.4863