Question

Test the hypothesis using the P-value approach. Be sure to verify the requirements of the test. Ho:p=0.74 versus H1:p(not equal) to 0.74 N= 500, x= 360, a= 0.05 Is npo (1-po)_>10? A. No, because np0(1-p0)=? B. Yes, because np0(1-p0)=?.

Now Find P (with carrot on top)=?

Find the test statistic z0=?

Find the P-value=?

State the conclusion of the hypothesis test.

Answer 1

Answer)

Null hypothesis Ho : P = 0.74

Alternate hypothesis Ha : P not equal to 0.74

N = 500

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

And n*p*(1-p) > 10

N*p = 370

N*(1-p) = 130

N*po*(1-po) = 96.2 > 10.

So, yes as npo*(1-po) > 10

All the conditions are met so we can use standard normal z table to estimate the P-Value

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

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

Observed P = 360/500

Claimed P = 0.74

N = 500

After substitution

Z = -1.02

From z table, P(z<-1.02) = 0.1539

As the test is two tailed

P-value = 2*0.1539 = 0.3078

As the obtained p-value is greater than the given significance 0.05

We fail to reject the null hypothesis Ho

So, we do not have enough evidence to conclude that p is not equal to 0.74