Question

Angela and Mary Anne feel like their school is very Democratic, more so than most places in the country. They survey to find that of 145 students, 98 identify as Democrats. Using the current congressional percentage (53%) as a point of comparison, and significance level 0.04, answer the following.

Step 1 of 6: What type of hypothesis test should be performed here?

Step 2 of 6: State the null hypothesis.

Step 3 of 6: State the alternative hypothesis.

Step 4 of 6: Perform the appropriate test and state your p-value.

Step 5 of 6: Choose your conclusion and the appropriate reasoning.

Step 6 of 6: Choose the appropriate interpretation of your conclusion.

Answer 1

Answer)

Step 1:

N= 145

P = 98/145

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 = 98

N*(1-p) = 47

Both the conditions are met so we can use standard normal z table to conduct the test

Step 2)

Ho : P = 0.53

Step 3)

Ha : P > 0.53

Step 4)

Test statistics z = (oberved p - claimed p)/standard error

Standard error = √{claimed p*(1-claimed p)/√n

Observed P = 98/145

Claimed p = 0.53

N = 145

Z = 3.52

From z table, P(Z>3.52) = 0.0002

P-value = 0.0002

Step 5)

As the obtained P-Value is less than the given significance level, we reject the null hypothesis

Step 6)

So we do have enough evidence to support the claim.