Question

1) If n = 250 and ˆ p = .44 , find a 95% confidence interval.

• [0.378, 0.502]
• [0.438, .442]
• [0.388, .492]
• [0.436, 0.444]

2) Which of the following is a condition for the sample proportion to be normally distributed?

• n≥30n≥30
• n≥10n≥10
• np(1−p)≥10
• np(1−p)≥30

Answer 1

using excel>addin>phstat>confidence interval

we have

Confidence Interval Estimate for the Proportion
Data
Sample Size	250
Number of Successes	110
Confidence Level	95%
Intermediate Calculations
Sample Proportion	0.44
Z Value	-1.9600
Standard Error of the Proportion	0.0314
Interval Half Width	0.0615
Confidence Interval
Interval Lower Limit	0.378
Interval Upper Limit	0.5015

1) a 95% confidence interval.

• [0.378, 0.502]

2) the condition for the sample proportion to be normally distributed is

• np(1−p)≥10