Question

1. a) Time Magazine states that the drop out rate for high school seniors is ten percent. You conduct a test to see if the drop out rate for high school seniors is actually more than ten percent.  One hundred high school seniors were randomly selected to see if they had dropped out.  The number of these high school seniors who dropped out is 15. Determine the p-value using test statistic, z=1.67.  Draw the graph. (α =0.01)

b) Time Magazine states that the drop out rate for high school seniors is ten percent. You conduct a test to see if the drop out rate for high school seniors is actually more than ten percent.  One hundred high school seniors were randomly selected to see whether they dropped out.  The number of these high school seniors who dropped out is 5.  Use the information and answer from question 1 to make a decision. What is the decision? Explain. (α = .01)   

c) State the proper conclusion for this hypothesis test

2. a) The Maryland Department of Health claims that the proportion of heroin users in Maryland that have been infected by HIV is five percent. Suppose a researcher wants to show that this claim is not true.  The researcher randomly selects 100 Maryland heroin users and finds that 80 have been infected with HIV. Determine the p-value using the test statistic, z= -2.11. Draw the graph.(α = 0.1)

b) The Maryland Department of Health claims that the proportion of heroin in Maryland that have been infected by HIV is four percent. Suppose a researcher wants to show that this claim is not true.  The researcher randomly selects 10000 Maryland heroin users and finds that 80 have been infected with HIV. Use the information and answer from question 2 to make a decision. What is the decision?  Explain. (α = 0.1)

c) State the proper conclusion for this hypothesis test

Answer 1

1)a) P-value = P(Z > 1.67)

                 = 1 - P(Z < 1.67)

                 = 1 - 0.9525

                 = 0.0475

b) H₀: p = 0.1

    H₁: p > 0.1

= 5/100 = 0.05

The test statistic is

P-value = P(Z > -1.67)

            = 1 - P(Z < -1.67))

            = 1 - 0.0475

            = 0.9525

Since the P-value is greater than the significance level (0.9525 > 0.01), so we should not reject the null hypothesis.

c) At 0.01 significance level, there is not sufficient evidence to conclude that the drop out rate for high school seniors is actually more than ten percent.

2)a) P-value = 2 * P(Z < -2.11)

                  = 2 * 0.0174

                  = 0.0348

b) H₀: p = 0.04

    H₁: p 0.04

= 80/10000 = 0.008

The test statistic is

P-value = 2 * P(Z < -16.33)

            = 2 * 0.0000 = 0.0000

Since the P-value is less than the significance level(0.0000 < 0.1), so we should reject the null hypothesis.

c) At 0.10 significance level, there is not sufficient evidence to support the claim that the proportion of heroin in Maryland that have been infected by HIV is four percent.