Question

In a survey of 444 HIV-positive smokers, 205 reported that they had used a nicotine patch to try to quit smoking. Can you conclude that less than half of HIV-positive smokers have used a nicotine patch? Use the α=0.05 level of significance and the P-value method with the table.

1)  State the null and alternate hypotheses.

The null hypothesis, H0, says that half of HIV-positive smokers have used a nicotine patch. Therefore we have

H0:

We are interested in knowing whether less than half of HIV-positive smokers have used a nicotine patch. Therefore, the alternate hypothesis is

H1:

right tailed,  Left tailed or two tailed?

2)  Compute the test statistic z=?

3) Compute the P-value. . Round the answer to four decimal places.

4) Determine whether to reject H0.

5) State a conclusion.

At the α=0.05  level of significance, there is or is not enough evidence to conclude that less than half of HIV-positive smokers have used a nicotine patch

Answer 1

n= 444, x= 205, P = 50% = 0.50

= 0.05

1)

The null and alternative hypothesis is

Ho: P = 0.50

H1: P <  0.50

Left tailed

2)

formula for test statistics is

z = -1.614

test statistics: z = -1.61

3)

calculate P-Value

P-Value = P(z < -1.61)

using z table we get

P(z < -1.61) = 0.0537

P-Value = 0.0537

4)

decision rule is

Reject Ho if ( P-value ) ( )

here, ( P-value= 0.0537 ) > ( = 0.05)

Hence, we can say,

Do not reject the null hypothesis ( Ho ).

5)

there is not enough evidence to conclude that less than half of HIV-positive smokers have used a nicotine patch At the α=0.05  level of significance.