Question

You wish to test the following claim (HaHa) at a significance level of ?=0.002.

      Ho:p=0.18
      Ha:p?0.18

You obtain a sample of size n=435 in which there are 73 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...

less than (or equal to) ??

greater than ??

This test statistic leads to a decision to...

reject the null

accept the null

fail to reject the null

As such, the final conclusion is that...

There is sufficient evidence to warrant rejection of the claim that the population proportion is not equal to 0.18.

There is not sufficient evidence to warrant rejection of the claim that the population proportion is not equal to 0.18.

The sample data support the claim that the population proportion is not equal to 0.18.

There is not sufficient sample evidence to support the claim that the population proportion is not equal to 0.18.

Answer 1

a) The test statistic here is computed as:

Therefore -0.661 is the test statistic value here.

b) As this is a two tailed test, the p-value is obtained from the standard normal tables as:

p = 2P( Z < -0.661 ) = 2*0.2542 = 0.5084

Therefore 0.5084 is the required p-value here.

c) The p-value here is 0.5084 > 0.002 which is the level of significance. Therefore the p-value is greater than

d) The test is not significant as the p-value is higher, therefore fail to reject the null hypothesis here.

e) Therefore as the test is not significant, there is not sufficient sample evidence to support the claim that the population proportion is not equal to 0.18.