Question

Conduct a hypothesis test (using either the p-Value Approach or the Critical Value Approach) to determine if the proportion of all recent clients is more dissatisfied than the traditional level of dissatisfaction. Use α = 0.08. Do not forget to include the correctly worded hypotheses and show all the steps required to conduct the hypothesis test. 92 out of sample of 200 were dissatisfied

Answer 1

Here we want to hypothesis test (using either the p-Value Approach or the Critical Value Approach) to determine if the proportion of all recent clients is more dissatisfied than the traditional level of dissatisfaction.

Let's assume that the proportion of the traditional level of dissatisfaction = 0.40

So null hypothesis is H₀ : P= 0.40

and alternative hypothesis is H₁ : P > 0.40

We can used one sample proportion z test.

Let' write given information.

n = sample size = 200

x = number of clients who are dissatisfied = x = 92.

level of significance = 0.08

Using minitab.

The command for one sample proportion z test in minitab is

Stat>>>Basic statistics>>>1-proportion...

Then click on summarized data

number of events = x = 92

Number of trials = n = 200

Click on "Perform hypothesis test

Hypothesized proportion = P = 0.40 (because under the null hypothesis P = 0.40)

then click on option

Level of confidence in percentage = c = ( 1- )*100 = = (1 - 0.08)*100 = 92.0

so put "Confidence level " = 92.0

Alternative = Greater than

then click on "Use test and interval based on normal approximation"

Then click on OK and again click on OK

So we get the following output

From the above output, we get p-value as:

P-value = 0.042

Decision rule:

1) If p-value < level of significance (alpha) then we reject null hypothesis

2) If p-value > level of significance (alpha) then we fail to reject null hypothesis.

Here p value = 0.042 > 0.08 so we used first rule.

That is we reject null hypothesis

Conclusion: At 8% level of significance there are sufficient evidence to say that the sample data indicates that the proportion of all recent clients is more dissatisfied than the traditional level of dissatisfaction.