Question

You wish to test the following claim (HaHa) at a significance level of α=0.001α=0.001.

      Ho:p=0.58Ho:p=0.58
      Ha:p≠0.58Ha:p≠0.58

You obtain a sample of size n=720n=720 in which there are 455 successful observations.

Determine the test statistic formula for this test.

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) αα
• greater than αα

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 0.58.
• There is not sufficient evidence to warrant rejection of the claim that the population proportion is not equal to 0.58.
• The sample data support the claim that the population proportion is not equal to 0.58.
• There is not sufficient sample evidence to support the claim that the population proportion is not equal to 0.58.

Answer 1

P = X / n = 455/720 = 0.6319
Test Statistic :-
Z = ( P - P0 ) / ( √((P0 * q0)/n)
Z = ( 0.6319 - 0.58 ) / ( √(( 0.58 * 0.42) /720))
Z = 2.824

P value = 2 * P ( Z > 2.824 ) = 0.0047 ( From Z table )

Reject null hypothesis if P value < α = 0.001
Since P value = 0.0047 > 0.001, hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0

greater than αα

fail to reject the null

There is sufficient evidence to warrant rejection of the claim that the population proportion is not equal to 0.58.