A certain drug is used to treat asthma. In a clinical trial of the​ drug, 20 of 301 treated subjects experienced

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

First identify the null and alternative hypotheses.

Identify the specific claim or hypothesis to be​ tested, and put it in symbolic form.

The claim to be tested is

p less than 0.08

.

Give the symbolic form that must be true when the original claim is false.

p greater than or equals 0.08

Of the two expressions obtained

​(p less than 0.08 and p greater than or equals 0.08​), let the alternative hypothesis H 1

be the one not containing equality.

Let the null hypothesis H0 be the symbolic expression that the parameter equals the fixed value being considered. Based on​ this, the hypotheses are as shown below.

H0: p equals 0.08

H1: p less than 0.08

The fact that the alternative hypothesis uses the less than​ symbol,

less than​, indicates that the region that supports the alternative hypothesis is to the left.

Conclude a​ left-tailed test because the test being performed is for  p less than 0.08

.

b. What is the test​ statistic?

The relevant sample statistic transformed to a standardized score is called the test statistic. Refer to the hypothesis test data given for the test statistic.

Determine the test​ statistic, rounding to two decimal places.

z  = - 0.87

c. What is the​ P-value?

The​ P-value is the probability of getting a value of the test statistic that is at least as extreme as the one representing the sample​ data, assuming that the null hypothesis is true. Refer to the hypothesis test data given for the​ p-value.

Determine the​ P-value, rounding to four decimal places.

​P-value = 0.1930

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

The null hypothesis was determined in part​ (a) above as

H0: p  =  0.08

.

Consider the significance​ level,

alpha

​,

and the​ P-value to decide if the null​ hypothesis,

Upper H 0

​,

should be rejected. If the​ P-value is less than or equal to the significance​ level, reject the null hypothesis. If the​ P-value is greater than the significance​ level, fail to reject the null hypothesis.

e. What is the final​ conclusion?

Use the results regarding the null hypothesis to address the original claim.

The final conclusion should say whether or not there is sufficient evidence to support the original claim.