Question

In a recent poll of 1200randomly selected​ adults, a​ president's approval rating stood at 45%. ​a) Make a 95​% confidence interval for his approval rating by all adults in the country. ​b) Based on the confidence​ interval, test the null hypothesis that 45​% of the country approved of the way he was handling his job at that time.

Answer 1

Answer)

N = 1200

P = 0.45

First we need to check the conditions of normality that is if n*p and n*(1-p) both are greater than 5 or not

N*p = 540

N*(1-p) = 660

Both the conditions are met so we can use standard normal z table to estimate the interval

Critical value z from z table for 95% confidence level is 1.96

Margin of error (MOE) = Z*√P*(1-P)/√N

Z = 1.96

P = 0.45

N = 1200

AFTER SUBSTITUTION

MOE = 0.02814835696

Confidence interval is given by

P-MOE < P < P+MOE

0.42185164303< P < 0.47814835696

B)

Null hypothesis Ho : P = 0.45

Alternate hypothesis Ha : P not equal to 0.45

As the confidence interval contains the null hypothesised value 0.45

We fail to reject the null hypothesis