Question

Information about a sample is given. Assume that the sampling distribution is symmetric and bell-shaped. "p-hat"= 0.34 and the standard error is 0.08.

a)  Indicate the parameter being estimated.

b) Use the information to give a 95% confidence interval.

The 95% confidence interval is (blank) to (blank)

Answer 1

Solution:

a)

Population proportion i.e. p

b)

c = 95% = 0.95

= 1- c = 1- 0.95 = 0.05

  /2 = 0.05 2 = 0.025 and 1- /2 = 0.975

Search the probability 0.975 in the Z table and see corresponding z value

= 1.96   

Now , the margin of error is given by

E = * Standard Error = 1.96 * 0.08 = 0.1568

Now , = 0.34

Now , confidence interval for mean() is given by:

( - E ) <   <  ( + E)

(0.34 - 0.1568)   <   <  (0.34 + 0.1568)

0.1832 <   <  0.4968

The 95% confidence interval is 0.1832   to 0.4968