Question

77) According to the National Institute on Alcohol Abuse and Alcoholism (NIAAA) and the National Institutes of Health (NIH), 41% of college students nationwide engage in "binge-drinking" behavior: having five or more drinks on one occasion during the past two weeks. A college president wonders if the proportion of students enrolled at her college who binge drink is actually lower than the national proportion. In a commissioned study, 347 students are selected randomly from a list of all students enrolled at the college. Of these, 130 admit to having engaged in binge drinking. The college president is more interested in testing her belief that the proportion of students at her college who engage in binge drinking is lower than the national proportion of 0.41. What is the P-value? (Round your answer to four decimal places.)
P-value =

78) The Dow Jones Industrial Average (DJIA) high values and the total number of points scores in the Super Bowl were recorded for 20 different years. Software was used to find that the value of the linear correlation coefficient is r = 0.83.

Is there a linear correlation at the α = .05 level between DJIA high value and Super Bowl points?

A) Yes, because the absolute value of 0.83 is less than the critical value.

B) Yes, because the absolute value of 0.83 is greater than the critical value.  

C) No, because the absolute value of 0.83 is less than the critical value.

D) No, because the absolute value of 0.83 is greater than the critical value

Answer 1

77) Let p be the true proportion of students enrolled at her college who binge drink. The college president is more interested in testing her belief that the proportion of students at her college who engage in binge drinking is lower than the national proportion of 0.41. That is she wants to test if p<0.41. This would be the alternative hypothesis as the alternative always has one of

The hypotheses are

In a commissioned study, 347 students are selected randomly from a list of all students enrolled at the college. Of these, 130 admit to having engaged in binge drinking.

That is

n=347 is the sample size

is the sample proportion of students having engaged in binge drinking

The hypothesized value of p is

The standard error of proportions is

Since

are both greater than 5, we can use normal distribution as the sampling distribution of proportions

The test statistic is

This is a left tailed test (The alternative hypothesis has "<")

The p-value is the area under the standard normal curve for z less than the test statistic.

What is the P-value? (Round your answer to four decimal places.)
ans: P-value = 0.0901

We will reject the null hypothesis, if the p-value is less than the significance level.

If we assume a significance level of alpha=0.05, we can see that the p-value is not less than 0.05. Hence we do not reject the null hypothesis.

There is not sufficient evidence to support her belief that the proportion of students at her college who engage in binge drinking is significantly lower than the national proportion of 0.41.

78) The Dow Jones Industrial Average (DJIA) high values and the total number of points scores in the Super Bowl were recorded for 20 different years. Software was used to find that the value of the linear correlation coefficient is r = 0.83.

Is there a linear correlation at the α = .05 level between DJIA high value and Super Bowl points?

Let be the true linear correlation between DJIA high value and Super Bowl points. We want to test the following

The number of observations is n=20. The degrees of freedom are n-2=20-2=18

Using the following for  α = .05

This is a 2 tailed test (The alternative hypothesis has "not equal to")

The critical values are -0.444 and +0.444

We will reject the null hypothesis, if the  value of the linear correlation coefficient, r does not lie with in the interval -0.444 to  +0.444. In other words, if the absolute value of r is greater than 0.444 (the right critical value) then we reject the null hypothesis.

Here the absolute value of r is 0.83 and it is greater than 0.444. Hence we reject the null hypothesis. We conclude that there is a linear correlation at the α = .05 level between DJIA high value and Super Bowl points.

ans:

B) Yes, because the absolute value of 0.83 is greater than the critical value.