Question

According to the Center for Disease Control website, in 2011 at least 18% of high school students have smoked a cigarette. An Introduction to Statistics class in Davies County, KY conducted a hypothesis test at the local high school (a medium sized–approximately 1,200 students–small city demographic) to determine if the local high school’s percentage was lower. One hundred fifty students were chosen at random and surveyed. Of the 150 students surveyed, 82 have smoked. Use a significance level of 0.05 and using appropriate statistical evidence, conduct a hypothesis test and state the conclusions.

Short answer

Local high school’s proportion of students who smoke is less than 0.18

Step-by-step solution

State the null and alternate hypothesis. we have to conduct hypothesis test if high school students of small city demographic take less than 18% of students have smoked, on average.

$H_0:p\ge 0.18;H_a:p<0.18$

Calculate the p-value using the normal distribution for proportions: 

$p-value=1$

In one to two complete sentences, explain what the p-value means for this problem. If the null hypothesis is true (the proportion is 0.18), then there is a 1.0000 probability that the sample (estimated) proportion is 0.547 or more.

Compare α and the p-value:Indicate the correct decision (“reject” or “do not reject” the null hypothesis), the reason for it, and write an appropriate conclusion, using complete sentences.

alpha	decision	reason for decision
0.05	Do not reject the null hypothesis.	$p-value>0.05$

Conclusion: At the 5% level of significance, there is not enough evidence to conclude that the local high school’s proportion of students who smoke is less than 0.18.