Question

1. Large Sample Proportion Problem. A survey was conducted on high school marijuana use. Of the 2266 high school students surveyed, 970 admitted to smoking marijuana at least once.  A study done 10 years earlier estimated that 45% of the students had tried marijuana. We want to conduct a hypothesis test to see if the true proportion of high school students who tried marijuana is now less than 45%.   Use alpha = .01.
What is the conclusion for this test?

A)Based on a tests statistic that is not in the rejection region for alpha = .01, we failed to reject the null hypothesis.

B)The p-value was below .05, therefore we failed to reject the null hypothesis.

C)The p-value was below .01, therefore we failed to reject the null hypothesis.

D)Based on a p-value less than .01, we would reject the null hypothesis and conclude the rate is now lower than 45.

2. Large Sample Proportion Problem.  Surveys were conducted in multiple countries and respondents were asked if they felt political news was reported fairly. The data for the United States is that out of 1,000 sampled, 470 indicated yes, they felt political news was reported fairly. Suppose we construct a 99% confidence interval and the upper and lower bounds are .4293 to .5107.

What can I conclude about a two-tailed hypothesis test where Ho: P=.5 and alpha is .01?

A)I would fail to reject the Null Hypothesis that P = .5

B)I don’t have enough information to make a conclusion.

C)I would be able to reject the Null Hypothesis that P = .5

D)I would be able to reject the Null Hypothesis that P=.5, but only for a one-tailed test.

3. Large Sample Proportion Problem. A survey was conducted on high school marijuana use. Of the 2266 high school students surveyed, 970 admitted to smoking marijuana at least once.  

The standard error for a confidence interval for this proportion would be:

A) It depends upon the Alternative Hypothesis

B) (.4237*.5763)/2266

C) (.4237*.5763)/SQRT(2266)

D) SQRT((.4237*.5763)/2266)

4. Large Sample Proportion Problem.  Surveys were conducted in multiple countries and respondents were asked if they felt political news was reported fairly. The data for the United States is that out of 1,000 sampled, 470 indicated yes, they felt political news was reported fairly. Suppose we want to construct a 99% confidence interval.

What is the z-value we would use?

A) 1.675 B) 1.96 C) 2.33 D) 2.576

5. Large Sample Proportion Problem.  Surveys were conducted in multiple countries and respondents were asked if they felt political news was reported fairly. The data for the United States is that out of 1,000 sampled, 470 indicated yes, they felt political news was reported fairly. Suppose we want to determine if the proportion for the U.S. is below .50.

What is the critical value I would use for alpha = .01?

A) -2.576 B) -2.33 C) -1.96 D) 2.576

Answer 1

#1.
pcap = 970/2266 = 0.4281

Test statistic,
z = (0.4281 - 0.45)/sqrt(0.45*0.55/2266) = -2.0955
p-value = 0.0181

Based on a tests statistic that is not in the rejection region for alpha = .01, we failed to reject the null hypothesis.
Option A

#2.
The hypothesised proportion 0.5 is included in the CI, hence we fail to reject the null hypothesis.
I would fail to reject the Null Hypothesis that P = .5

#3.
SE = SQRT((.4237*.5763)/2266)

#4.
z-value = 2.576

#5.
B) -2.33