Question

Hw 28 #2

A recent poll of 2500 randomly selected 18-25-year-olds revealed that 290 currently use marijuana or hashish. According to a publication, 12.5 % of 18-25-year-olds were current users of marijuana or hashish in 1997. Do the data provide sufficient evidence to conclude that the percentage of 18-25-year-olds who currently use marijuana or hashish has changed from the 1997 percentage of 12.5 %? Use α=0.01 significance level.

test statistic z=

positive critical z score=

negative critical z score=

The final conclusion is

A. There is sufficient evidence to conclude that the percentage of 18-25-year-olds who currently use marijuana or hashish has changed from the 1997 percentage of 12.5 12.5 %.

B. There is not sufficient evidence to conclude that the percentage of 18-25-year-olds who currently use marijuana or hashish has changed from the 1997 percentage of 12.5 12.5 %.

Answer 1

Here we have given that,

n=number of randomly selected 18-25 year old in recent poll=2500

x: number of randomly selected 18-25-year-old revealed that currently, they use marijuana or hashish= 290

Now, we estimate the sample proportion as

=sample proportion randomly selected 18-25-year-old revealed that currently, they use marijuana or hashish

=

Claim: To check whether the proportion of 18-25 year olds who currently use marijuana or hashish has changed form the 1997 proportion of 0.125 i.e. 12.5%

The null and alternative hypothesis are as follows,

Versus

where p is the population proportion of 18-25-year-olds were current users of marijuana or hashish in 1997 = 12.5%=0.125

This is the two-tailed test.

Now, we can find the test statistic is as follows,

Z-statistics=

=

= -1.36

The test statistics is -1.36

Now we find the critical value,

= level of significance= 0.01

= Zcritical (0.005)

                              = 2.58 or -2.58 Using EXCEL software =(NORMSINV(probability =0.005))

The positive critical z score = 2.58

The negative critical z score = -2.58

Decision rule:

Reject Ho Null hypothesis if the test statistics is either larger than positive critical value or smaller than negative critical value otherwise fail to reject Ho.

Decision:

Here, Z-statistics (-1.36) < the Positive z-critical value (2.58)

i.e. we fail to reject the Null hypothesis Ho.

Conclusion:

There is sufficient evidence to conclude that the percentage of 18-25-year-olds who currently use marijuana or hashish has changed from the 1997 percentage of 12.5% i.e. 0.125