Question

Given below are the number of successes and sample size for a simple random sample from a population. x equals=6​, n equals=40​, 98​% level

a. Determine the sample proportion.

b. Decide whether using the​ one-proportion z-interval procedure is appropriate.

c. If​ appropriate, use the​ one-proportion z-interval procedure to find the confidence interval at the specified confidence level.

d. If​ appropriate, find the margin of error for the estimate of p and express the confidence interval in terms of the sample proportion and the margin of error.

Answer 1

Solution :

Given that,

n = 40

x = 6

Point estimate = sample proportion = = x / n = 6/40 = 0.150

1 - = 1- 0.15 = 0.850

Z_/2 = 2.326

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 2.326 * (0.150(1-.0.150) /40 )

= 0.131

A 98% confidence interval for population proportion p is ,

- E < p < + E

0.150- 0.131 < p < 0.150 + 0.131

0.019< p < 0.281

The 95% confidence interval for the population proportion p is : 0.019 , 0.281