Question

Consider the following hypotheses.

H0​: less than or equals 0.11

H1​: greater than 0.11

Given that p overbar equals 0.125​, n=120​, and alpha=0.01​, answer the following questions.

a. What conclusion should be​ drawn?

b. Determine the​ p-value for this test.

a. Determine the critical​ value(s) of the test statistic.

z alpha = ____

​Use a comma to separate answers as needed. Round to two decimal places as​ needed.)

Calculate the test statistic.

zp = _____ ​

(Round to two decimal places as​ needed.)

What conclusion should be​ drawn?

A. Do not reject Upper H0. There is sufficient evidence that p is greater than 0.11.

B. Do not reject Upper H0. There is insufficient evidence that p is greater than 0.11.

C. Reject Upper H0. There is sufficient evidence that p is greater than 0.11.

D. Reject Upper H0. There is insufficient evidence that p is greater than 0.11.

b.​ Find p-value

p-value = _____

​(Round to three decimal places as​ needed.)

Answer 1

Consider the hypotheses.

H0​: less than or equals 0.11

H1​: greater than 0.11

Using parameter the hypothesis

The values provided in the above question are as

p overbar equals 0.125​, n=120​, and alpha=0.01

a. We determine the critical​ value(s) of the test statistic.

z alpha = 2.33

(Because the above test is right tailed test and alpha = =0.01 that is

we find the probability = 1 - = 1 - 0.01 = 0.99

probability = 0.99

We find the above probability using Excel function

=NORMSINV(probability)

Here, probability = 0.99

=NORMSINV(0.99) then press Enter, we get

=2.326348 2.33 (Round answer to two decimal places)

z alpha = 2.33

We calculate the test statistic using following formula

Using above values we get

(Round answer to two decimal places)

test statistic = =

What conclusion should be​ drawn?

Answer :- B. Do not reject Upper H0. There is insufficient evidence that p is greater than 0.11.

Because, We comparing the test statistic = = with z alpha = 2.33 and take decision about reject or do not reject H₀ using following way

1) If  test statistic    z alpha then we do not reject H₀

2) If test statistic   z alpha then we reject H₀

Here, test statistic = =    z alpha = 2.33

then we do not reject H₀.

That is, Do not reject Upper H0. There is insufficient evidence that p is greater than 0.11.

b.​ Find p-value

p-value = 0.702 When we use test statistic = =

or

p-value = 0.700 When we use test statistic =

We find p-value for the above test statistic value = 0.53 using Excel function

=NORMSDIST(z)

Here, z = test statistic = =

=NORMSDIST(0.53) then press Enter we get

=0.701944 0.702 (Round answer to three decimal places)

p-value = 0.702

Or

We find p-value for the above test statistic value = using Excel function

=NORMSDIST(z)

Here, z = test statistic =  

=NORMSDIST(0.525158665) then press Enter we get

=0.700264 0.700 (Round answer to three decimal places)

p-value = 0.700

Summary :-

a. z alpha = 2.33

test statistic = =

What conclusion should be​ drawn?

Answer :- B. Do not reject Upper H0. There is insufficient evidence that p is greater than 0.11.

p-value = 0.702 When we use test statistic = = (Round up to two decimal places)

[If you need to calculate the p-value without rounding test statistic then use answer of p-value as below]

p-value = 0.700 When we use test statistic = (Without rounding the answer)