Question

15.

Suppose 221 subjects are treated with a drug that is used to treat pain and 54 of them developed nausea. Use a 0.10 significance level to test the claim that more than 20​% of users develop nausea.

___________________

Identify the null and alternative hypotheses for this test. Choose the correct answer below.

A.

H0​:

p>0.20

H1​:

p=0.20

B.

H0​:

p=0.20

H1​:

p>0.20

C.

H0​:

p=0.20

H1​:

p<0.20

D.

H0​:

p=0.20

H1​:

p≠

_____________________

Identify the test statistic for this hypothesis test.

The test statistic for this hypothesis test is ​(Round to two decimal places as​ needed.)

Identify the​ P-value for this hypothesis test.

The​ P-value for this hypothesis test is ​(Round to three decimal places as​ needed.)

_____________________________

Identify the conclusion for this hypothesis test.

A.

Fail to reject

H0.

There

is not

sufficient evidence to warrant support of the claim that more than

20​%

of users develop nausea.

B.

Reject

H0.

There

is not

sufficient evidence to warrant support of the claim that more than

20​%

of users develop nausea.

C.

Reject

H0.

There

is

sufficient evidence to warrant support of the claim that more than

20​%

of users develop nausea.

D.

Fail to reject

H0.

There

is

sufficient evidence to warrant support of the claim that more than

20​%

of users develop nausea.

Answer 1

Solution :

Given that,

= 0.20

1 - = 0.80

n = 221

x = 54

Level of significance = = 0.10

Point estimate = sample proportion = = x / n = 0.24

This a right (One) tailed test.

The null and alternative hypothesis is,

B)

Ho: p = 0.20

Ha: p 0.20

Test statistics

z = ( - ) / *(1-) / n

= ( 0.24 - 0.20) / (0.20*0.80) /221

= 1.65

P-value = P(Z > z )

= 1 - P(Z < 1.65 )

= 0.050

Therefore, P-value < 0.10, reject the null hypothesis.

C.

Reject H0. There is sufficient evidence to warrant support of the claim that more than 20​% of users develop nausea.