Question

One research study of illegal drug use among​ 12- to​ 17-year-olds reported a decrease in use​ (from 11.4% in​ 1997) to

9.89.8​%

now. Suppose a survey in a large high school reveals​ that, in a random sample of

1 comma 0561,056

​students,

9393

report using illegal drugs. Use a 0.05 significance level to test the​ principal's claim that illegal drug use in her school is below the current national average.

Formulate the null and alternative hypotheses. Choose the correct answer below.

A.

Upper H 0H0​:

pless than<0.0980.098​,

Upper H Subscript aHa​:

pequals=0.0980.098

B.

Upper H 0H0​:

pequals=0.0980.098​,

Upper H Subscript aHa​:

pgreater than>0.0980.098

C.

Upper H 0H0​:

pgreater than>0.0980.098​,

Upper H Subscript aHa​:

pless than<0.0980.098

D.

Upper H 0H0​:

pequals=0.0980.098​,

Upper H Subscript aHa​:

pless than<0.0980.098

Find the test statistic.

zequals=nothing

​(Round to one decimal place as​ needed.)

Find the​ P-value for the found test statistic.

​P-valueequals=nothing

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

Now make a conclusion. Choose the correct answer below.

A.

There is sufficient evidence to support the claim that illegal drug use is below the national average.

B.

There is not sufficient evidence to support the claim that illegal drug use is below the national average.

C.

There is not enough information to make a conclusion.

Answer 1

we have to test whether the principal's claim that illegal drug use in her school is below the current national average.

So, it is a one tailed hypothesis test

Option D

using TI 84 calculator

press stat then tests then 1-PropZtest

enter the data

po = 0.098

x = 93

n = 1056

prop < po

press enter, we get

z statistic = -1.1

p value = 0.1357

it is clear that the p value is greater than 0.05 significance level

so,we failed to reject the null hypothesis

therefore, option B is correct answer