Question

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

      Ho:p=0.82Ho:p=0.82
      Ha:p<0.82Ha:p<0.82

You obtain a sample of size n=695n=695 in which there are 540 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 critical value for this test? (Report answer accurate to three decimal places.)
critical value =

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

The test statistic is...

in the critical region

not in the critical region

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 0.82.

There is not sufficient evidence to warrant rejection of the claim that the population proportion is less than 0.82.

The sample data support the claim that the population proportion is less than 0.82.

There is not sufficient sample evidence to support the claim that the population proportion is less than 0.82.

Answer 1

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: P = 0.82
Alternative hypothesis: P < 0.82
Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected only if the
sample proportion is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.001. The test method, shown in
the next section, is a one-sample z-test.
Analyze sample data. Using sample data, we calculate the standard deviation (S.D) and compute the z-
score test statistic (z).
S.D = sqrt[ P * ( 1 - P ) / n ]
S.D = 0.01457
z = (p - P) / S.D
z = - 2.95

z_critical = - 3.09

Rejection region is z < - 3.09
where P is the hypothesized value of population proportion in the null hypothesis, p is the sample
proportion, and n is the sample size.

Interpret results. Since the z-value (-2.95) does not lie in the rejcetion region, we have to accept the
null hypothesis.

fail to reject the null hypothesis.

There is not sufficient sample evidence to support the claim that the population proportion is less than 0.82.