1. Suppose you want to estimate with 95% confidence the difference between the mean length of the zucchinis of two varieties of (allowing them to grow the same number of days and under the same conditions). The two varieties are Mr. Greens Zucchini and Mountains Zucchini. Assume by prior research that the population standard deviations for are Mr. Greens Zucchini and Mountains Zucchini are 0.35 inches and 0.45 inches. Calculate the confidence interval.

2. A student wants to assess whether her dog Muffin tends to chase her blue ball more often than she chases her red ball. The student rolls both a blue ball and a red ball at the same time and observes which ball Muffin chooses to chase. Repeating this process a total of 96 times, the student finds that Muffin chased the blue ball 52 times and the red ball 44 times.

a. What are the observational units in this study?

b. What is the variable in this study?

c. State the appropriate null and alternative hypotheses, in words and in symbols.

d. Are the technical conditions met in order to conduct a test?

3. Suppose you want to estimate the proportion of people in your community who would choose Thin Mints as their favorite Girl Scout cookie. Also suppose previous studies have shown this proportion to be around 0.3.

a. Determine how many people you would have to sample in order to estimate this proportion to within 0.025 with 90% confidence.

4. Students in an introductory statistics class were asked to report the age of their mothers when they were born. Summary statistics include

Sample size: 28 students

Sample mean: 29.643 years

Sample standard deviation: 4.564 years

a. Calculate the standard error of this sample mean.

b. Determine and interpret a 90% confidence interval for the mothers mean age (at students birth) in the population of all students at this university.