Question

You are conducting a study to see if the proportion of students who prefer tests rather than projects is significantly more than 0.89. You use a significance level of α=0.002.

      H0:p=0.89
      H1:p>0.89

You obtain a sample of size n=447n=447 in which there are 402 successes.

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 p-value leads to a decision to...

• reject the null
• accept the null
• fail to reject the null

As such, the final conclusion is that...
a. There is sufficient evidence to warrant rejection of the claim that the proportion of students who prefer tests rather than projects is more than 0.89.

b.There is not sufficient evidence to warrant rejection of the claim that the proportion of students who prefer tests rather than projects is more than 0.89.

c.The sample data support the claim that the proportion of students who prefer tests rather than projects is more than 0.89.

d.There is not sufficient sample evidence to support the claim that the proportion of students who prefer tests rather than projects is more than 0.89.

Answer 1

The following information is provided: The sample size is n = 447, the number of favorable cases is X =402, and the sample proportion is p bar= X/ N = 402 /447 = 0.8993 and the significance level is α=0.002

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: p = 0.89

H1 :p > 0.89

(2) Test Statistics

The z-statistic is computed as follows:

(3) Decision about the null hypothesis

Using the P-value approach: The p-value is p = 0.2642, and since p = 0.2642 ≥ 0.002, it is concluded that the null hypothesis is not rejected.

p-value is p = 0.2642

p-value is greater than α

fail to reject the null

final conclusion : Answer : option ( a )

There is sufficient evidence to warrant rejection of the claim that the proportion of students who prefer tests rather than projects is more than 0.89.