Question

A recent drug survey showed an increase in the use of drugs and alcohol among local high school seniors as compared to the national percent. Suppose that a survey of 100 local seniors and 100 national seniors is conducted to see if the proportion of drug and alcohol use is higher locally than nationally. Locally, 69 seniors reported using drugs or alcohol within the past month, while 60 national seniors reported using them. Conduct a hypothesis test at the 5% level of significance.

What is the p-value? (Round your answer to four decimal places.)

Explain what the p-value means for this problem:

a)If H0 is false, then there is a chance equal to the p-value that the proportion of students who use drugs and alcohol locally is at least 0.09 more than the proportion of students who use drugs and alcohol nationally.

b)If H0 is true, then there is a chance equal to the p-value that the proportion of students who use drugs and alcohol locally is 0.09 less than the proportion of students who use drugs and alcohol nationally.

c)If H0 is true, then there is a chance equal to the p-value that the proportion of students who use drugs and alcohol locally is at least 0.09 more than the proportion of students who use drugs and alcohol nationally.

d)If H0 is false, then there is a chance equal to the p-value that the proportion of students who use drugs and alcohol locally is 0.09 less than the proportion of students who use drugs and alcohol nationally.

Explain how you determined which distribution to use. a) The t-distribution will be used because the samples are dependent. b) The standard normal distribution will be used because the samples involve the difference in proportions c) The t-distribution will be used because the samples are independent and the population standard deviation is not known. d) The standard normal distribution will be used because the samples are independent and the population standard deviation is known.

Answer 1

p value =0.0918

c)If H0 is true, then there is a chance equal to the p-value that the proportion of students who use drugs and alcohol locally is at least 0.09 more than the proportion of students who use drugs and alcohol nationally.

b) The standard normal distribution will be used because the samples involve the difference in proportions