Question

A certain drug is used to treat asthma. In a clinical trial of the​ drug,

24

of

260

treated subjects experienced headaches​ (based on data from the​manufacturer). The accompanying calculator display shows results from a test of the claim that less than

11%

of treated subjects experienced headaches. Use the normal distribution as an approximation to the binomial distribution and assume a

0.01

significance level to complete parts​ (a) through​ (e) below.

​1-PropZTest
	prop <0.11
	z=-0.911758481
	p=0.1809479355
	ModifyingAbove p=0.0923076923
	n=260

a. Is the test​ two-tailed, left-tailed, or​ right-tailed?

​Left-tailed test

Right tailed test

​Two-tailed test

b. What is the test​ statistic?

z=nothing

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

c. What is the​ P-value?

​P-value=nothing

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

d. What is the null​ hypothesis, and what do you conclude about​ it?

Identify the null hypothesis.

A.

Upper H 0 : p not equals 0.11H0: p≠0.11

B.

Upper H 0 : p greater than 0.11H0: p>0.11

C.

Upper H 0 : p equals 0.11H0: p=0.11

D.

Upper H 0 : p less than 0.11H0: p<0.11

Decide whether to reject the null hypothesis. Choose the correct answer below.

A.

Reject

the null hypothesis because the​ P-value is

less than or equal to

the significance​ level,

α.

B.

Fail to reject

the null hypothesis because the​ P-value is

less than or equal to

the significance​ level,

α.

C.

Reject

the null hypothesis because the​ P-value is

greater than

the significance​ level,

α.

D.

Fail to reject

the null hypothesis because the​ P-value is

greater than

the significance​ level,

α.

e. What is the final​ conclusion?

A.There

is not

sufficient evidence to warrant rejection of the claim that less than

11​%

of treated subjects experienced headaches.

B.There

is

sufficient evidence to warrant rejection of the claim that less than

11​%

of treated subjects experienced headaches.

C.There

is

sufficient evidence to support the claim that less than

11​%

of treated subjects experienced headaches.

D.There

is not

sufficient evidence to support the claim that less than

11​%

of treated subjects experienced headaches.

Answer 1

Solution :

This is the left tailed test .

The null and alternative hypothesis is

H₀ : p = 0.11

H_a : p < 0.11

= x / n = 24 / 260 = 0.0923

P₀ = 0.11

1 - P₀ = 0.89

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.0923 - 0.11/ [(011 * 0.89) /260 ]

= -0.91

P-value = 0.1809

= 0.01

P-value >

Fail to reject the null hypothesis .

D.

Fail to reject the null hypothesis because the​ P-value is greater than the significance​ level

A.There is not sufficient evidence to warrant rejection of the claim that less than 11​% of treated subjects

experienced headaches.