Question

Consider a drug testing company that provides a test for marijuana usage. Among 291tested​ subjects, results from 27subjects were wrong​ (either a false positive or a false​ negative). Use a 0.05 significance level to test the claim that less than 10 percent of the test results are wrong.

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

A.

Upper H 0

​:

pless than

0.1

Upper H 1

​:

pequals

0.1

B.

Upper H 0

​:

pequals

0.1

Upper H 1

​:

pless than

0.1

C.

Upper H 0

​:

pequals

0.1

Upper H 1

​:

pgreater than

0.1

D.

Upper H 0

​:

pequals

0.1

Upper H 1

​:

pnot equals

0.1

Identify the test statistic for this hypothesis test.

The test statistic for this hypothesis test is

nothing

.

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

Identify the​ P-value for this hypothesis test.

The​ P-value for this hypothesis test is

nothing

.

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

Identify the conclusion for this hypothesis test.

A.

Reject

Upper H 0

.

There

is

sufficient evidence to warrant support of the claim that less than

10

percent of the test results are wrong.

B.

Fail to reject

Upper H 0

.

There

is

sufficient evidence to warrant support of the claim that less than

10

percent of the test results are wrong.

C.

Reject

Upper H 0

.

There

is not

sufficient evidence to warrant support of the claim that less than

10

percent of the test results are wrong.

D.

Fail to reject

Upper H 0

.

There is not sufficient evidence to warrant support of the claim that less than10 percent of the test results are wrong.

Answer 1

Solution :

Given that ,

n = 291

x = 27

The null and alternative hypothesis is ,

Upper H0 : p = 0.10

Upper Ha : p < 0.10

This is the left tailed test .

= x / n = 27 / 291 = 0.0928

P0 = 10% = 0.10

1 - P0 = 1 - 0.10 = 0.90

Test statistic = z

= - P0 / [P0 * (1 - P0 ) / n]

= 0.0928 - 0.10 / [0.10 (1 - 0.10) / 291 ]

= -0.41

The test statistic = -0.41

P-value = 0.3408

The P - value = 0.341

= 0.05  

0.341 > 0.05  

P-value >

Fail to reject the null hypothesis .

Correct option :- D. Fail to reject Upper Ho

There is not sufficient evidence to warrant support of the claim that less than10 percent of the test results are wrong.