You want to estimate the proportion of kids between the ages of 12 and 15 who have tried marijuana. you take a random sample of 130 maryland students and find that 23% of the sample report having tried marijuana. last year, the federal government ran a much larger survey of 10,000 students and found that 29% reported ever using marijuana. test the null hypothesis that the true population proportion of maryland students who have smoked marijuana is 29% versus the alternative hypothesis that it is different than that. use a 3% significance level. interpret your result.

Let p represents the population proportion.

By considering the given information, we have

∵ the alternative hypothesis is two tailed , so the test is two-tailed test.

Given : For sample size :n= 130,  

Test statistic:

P-value (two -tailed test)=

Since , the p-value (0.131) is greater than the significance level (0.03), so we accept the null hypothesis.

Thus , we conclude that we have sufficient evidence to support the null hypothesis  that the true population proportion of Maryland students who have smoked marijuana is 29% .

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