Question

You wish to test the following claim (Ha Ha ) at a significance level of α=0.02 α=0.02 . Ho:p=0.63 Ho:p=0.63 Ha:p<0.63 Ha:p<0.63 You obtain a sample of size n=485 n=485 in which there are 283 successful observations. For this test, you should NOT use the continuity correction, and you should use the normal distribution as an approximation for the binomial distribution.

What is the test statistic for this sample? (Report answer accurate to three decimal places.)

test statistic =

What is the p-value for this sample? (Report answer accurate to four decimal places.)

p-value =

The p-value is?( pick one)

less than (or equal to) α

α greater than α

This test statistic leads to a decision to?(pick one)

reject the null

accept the null

fail to reject the null

As such, the final conclusion is that? (pick one)

There is sufficient evidence to warrant rejection of the claim that the population proportion is less than 0.63.

There is not sufficient evidence to warrant rejection of the claim that the population proportion is less than 0.63.

The sample data support the claim that the population proportion is less than 0.63.

There is not sufficient sample evidence to support the claim that the population proportion is less than 0.63.

Answer 1

Answer)

Ho: P = 0.63

Ha : P < 0.63

N = 485

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 = 305.55

N*(1-p) = 179

Both are greater than 5, so conditions are met and we can use standard normal z table to conduct the test.

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

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

Observed p = 283/485

Claimed p = 0.63

N = 485

Z = -2.12

Test statistics = -2.12

From z table, p(z<-2.12) = 0.0170

P-value = 0.017

As the obtained p-value is less than the given alpha (0.02)

We reject the null hypothesis.

There is sufficient evidence to warrant rejection of the claim that the population proportion is less than 0.63.