Question

Over the past few decades, public health officials have examined the link between weight concerns and teen girls' smoking. Researchers surveyed a group of 273 randomly selected teen girls living in Massachusetts (between 12 and 15 years old). After four years the girls were surveyed again. Sixty-three said they smoked to stay thin. Is there good evidence that more than thirty percent of the teen girls smoke to stay thin?

After conducting the test, your decision and conclusion are

a. Reject H0: There is sufficient evidence to conclude that more than 30% of teen girls smoke to stay thin.

b. Do not reject H0: There is not sufficient evidence to conclude that less than 30% of teen girls smoke to stay thin.

c. Do not reject H0: There is not sufficient evidence to conclude that more than 30% of teen girls smoke to stay thin.

d. Reject H0: There is sufficient evidence to conclude that less than 30% of teen girls smoke to stay thin.

Short answer

c. Do not reject H0: There is not sufficient evidence to conclude that more than 30% of teen girls smoke to stay thin.

Step-by-step solution

Find H0 and Ha: We want to test if Massachusetts girls take more than 30% to stay thin.

$H_0:p=0.30;H_a:p>0.30$

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
0.01	Do not reject H0	$p-value<0.01$

Conclusion: Do not reject H₀: There is not sufficient evidence to conclude that more than 30% of teen girls smoke to stay thin.