Question

You wish to test the following claim (HaHa) at a significance level of ?=0.01.

      Ho:p=0.3
      Ha:p<0.3

You obtain a sample of size n=452 in which there are 128 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 less than 0.3.

There is not sufficient evidence to warrant rejection of the claim that the population proportion is less than 0.3.

The sample data support the claim that the population proportion is less than 0.3.

There is not sufficient sample evidence to support the claim that the population proportion is less than 0.3.

Answer 1

The statistical software output for this problem is:

One sample proportion summary hypothesis test:
p : Proportion of successes
H₀ : p = 0.3
H_A : p < 0.3

Hypothesis test results:

Proportion	Count	Total	Sample Prop.	Std. Err.	Z-Stat	P-value
p	128	452	0.28318584	0.021554623	-0.78007207	0.2177

Hence,

Test statistic = -0.780

p - Value = 0.2177

The p - value is greater than ?

Fail to reject the null

There is not sufficient sample evidence to support the claim that the population proportion is less than 0.3. Option D is correct.