Question

A school conducts survey of nine-hundred random students and results show that four-hundred-eighty-five support Anna for class president. population proportion of surveyors --> "p"

test of... p= .5 vs p > .5

x= 485, n =900, sample p = .538889, 95% CI = (.506322, .571456), z-value = 2.33, p-val = .010

a. what is the sample proportion?

b. what is estimate of "p"?

c.what is standard error of sample prop and the standard deviation of sample prop?

d. what is the 95% CI for p, and 99% CI?

e. what is the null hypothesis being tested here, and the alternative hypothesis of test?

Answer 1

a. Sample proportion is the proportion of students support Anna for class president among the sample of 900 .

Which is sample p = 0.538889

b. Estimate of P is the sample proportion which is 0.538889

c. Standard deviation of sample proportion and standard error of sample proportion is the same thing. Which is

SE =

=

= 0.016616

d. 95% confidence interval of p is

( 0.506322 , 0.571456 )

The 99% confidence interval of p is

= Z = 2.576 for 99% confidence

= ( 0.538889 2.576×0.016616 )

= ( 0.496086 , 0.581692 )

e. The Null Hypothesis is being tested here

Ho : p = 0.5 , the population proportion is equal to 0.5

The alternative hypothesis is

Ha : p > 0.5 , the population proportion is more than 0.5