Question

1. (10pts) Suppose from a class survey of 35 students, 6 students states they believe in Bigfoot. Answer the following questions.

(a) Obtain a point estimate for the population proportion of students that believe in Bigfoot.

(b) Determine the critical value needed to construct a 98% confidence interval for the proportion of students that believe in Bigfoot.

(c) Determine the standard error estimate (SE-est) for the confidence interval.

(d) Construct a 98% confidence interval for the proportion of students that believe in Bigfoot.

(e) Interpret the 98% confidence interval you found in part (d) above.

Answer 1

n=35, x= 6,

a)

point estimate =0.1714

b)

now find the critical value for c=98% using t table

we get

Critical Value = 2.326

c)

formula for standard error is

SE-est = 0.0637

Standard error (SE-est)= 0.0637

d)

formula for confidence inteval is

0.0232338 < P < 0.3195662

Thus we get confidence interval as (0.023 , 0.320)

e)

Therefore we are 98% confident that the true proportion of students that believe in Bigfoot lies between 0.023 to 0.32.