Math, Statistics and Probability

1. Assume that population means are to be estimated from the sample described. Use the sample results to approximate the margin of error and 95% confidence interval.

Sample size: 1,083

Sample mean: 46,229

Sample standard deviation: 22,000

The margin of error is: 

Find the 95% confidence interval:

2. Same question like above but different Samples

Sample size: 1,062

Sample mean: 46,253

Sample Standard Deviation: 22,000

What is the margin of error:

What is the 95% confidence interval:

3. One research study of illegal drug use among 12- to 17-year-olds reported a decrease in use (from 11.4% in 1997) to 9.8% now. Suppose a survey in a high school reveals that, in a random sample of 1,043 students, 95 report using illegal drugs. Use a 0.05 significance level to test the principal's claim that illegal drug use in her school is below the current national average.

You must Formulate the null and alternative hypotheses:

Find the test statistic.

z= 

P-value:

Now make a conclusion: Is it enough evidence?

4. The assets (in billions of dollars) of the four wealthiest people in a particular country are 41, 33, 17, 16. Assume that samples of size 2 are randomly selected with replacement from this population of four values. 

A. What are the probability for these numbers:

1. 41, 37, 33, 29, 28.5, 25, 24.5, 17, 16.5, 16

B. Find the mean of the sampling distribution ( Round to two decimal places as needed)

C. Is the mean of the sampling distribution [ from part (b)] equal to the mean of the population of the four listed values? If so, are those means always equals?