A philosophy professor wants to find out whether the mean age of the men in his large lecture class is equal to the mean age of the women in his classes. After collecting data from a random sample of his students, the professor tested the hypothesis

A certain population is strongly skewed to the right. We want to estimate its mean, so we will collect a sample. Which should be true if we use a large sample rather than a small one?  I. The distribution of our sample data will be closer to normal.II. The sampling model of the sample means will be closer to normal.III. The variability of the sample means will be greater. 

Which is true about a 95% confidence interval based on a given sample?I. The interval contains 95% of the population.II. Results from 95% of all samples will lie in the interval.III. The interval is narrower than a 98% confidence interval would be. 

Depression A recent psychiatric study from the University of Southampton observed a higher incidence of depression among women whose birth weight was less than 6.6 pounds than in women whose birth weight was over 6.6 pounds. Based on a P-value of 0.0248 the researchers concluded there was evidence that low birth weights may be a risk factor for susceptibility to depression. Explain in context what the reported P-value means. 

We have calculated a confidence interval based upon a sample of n = 200. Now we want to get a better estimate with a margin of error only one fifth as large. We need a new sample with n at least…

A professor was curious about her students’ grade point averages (GPAs). She took a random sample of 15 students and found a mean GPA of 3.01 with a standard deviation of 0.534. Which of the following formulas gives a 99% confidence interval for the mean GPA of the professor’sstudents?

Use​ Green’s Theorem to evaluate the line integral

Find the directional derivative of the function

Evaluate the triple integral

Given the force field