pleas answerthe following questions:

1) The Fanshawe Student Union wants determine the proportion of students who experienced extreme level of stress during the past month. They want to be 95% confident of the result. And they want to use a sample that is large enough to estimate this proportion with a margin of error of 3.1%.

What minimum sample size should be used?

2)Cedar Shadows Marketing Inc. would like to add health benefits to their company benefits package. However, the owner of Cedar Shadows Marketing Inc. is concerned about the amount of expenses each employee would charge to the plan and she would like to know the amount on average all employees would spend on health care benefits. A random sample of 105 Cedar Shadow Marketing workers reveals the mean amount spent per worker family, last year on health benefits was $1232, with a standard deviation of $660 (Round all statistics and answer to four decimal places)

(a) Calculate and construct, the 95% confidence interval estimate for the average amount spent per family each year on health benefits. (3 points)

(b) INTERPRET YOUR RESULTS

(c) The confidence interval above was given to the owner of Cedar Shadows Marketing Inc. She had committed to being able to fund $1700 of health expenses per family. Is it possible that the population mean amount spent on health expenses could be $1700? EXPLAIN!

3)Mr. Big Candy Store makes a specialty chocolate bar called The Mr. Big Candy Bar. Each Mr. Big Candy Bar should be 6 inches long. The owner of the store Mr. Little has had customer complaints that the Mr. Big Candy Bar have a different length than the required 6 inches. Mr. Little takes a random sample of 36 different Mr. Big Candy Bars from the store and the average length of the Candy Bars was 6.5 inches, with a standard deviation of 1.1 inches. Using a 5% significance level, test the claim that the length of the Mr. Big Candy Bar is not the required 6 inches at the Mr. Big Candy Store. (Remember your units) (Round all statistics and answer to four decimal places) (7 points)

b)Why would or should Mr. Little care?

4)A Big Box executive wants to determine the proportion of customers that were satisfied with their purchase in the last month. From a random sample of 2,000 Big Box customers, 1,400 consumers stated that they were satisfied with their purchase. (Round all statistics and answer to four decimal places)

(a) Calculate and construct, the 95% confidence interval estimate for the proportion of Big Box customers who were satisfied with their purchase last month. (2 points)

(b) INTERPRET YOUR RESULTS (2 points)

(c) Is it reasonable to say that 75% of Big Box customers were satisfied with their purchase last month? EXPLAIN!

5) Using data from previous attendance records suggests that 45% of the people that visit the Toronto Zoo are children. A study by the Toronto Zoo surveyed 1,200 visitors and 588 of them were children. Can we say there has been an increase in the proportion of children visiting the Toronto Zoo? Use a 5% significance level.(Round all statistics and answer to four decimal places) [7 points]

b) Does your answer change if the significance level is changed to 1%?

6)A fast food restaurant wants to know how much an automated beverage machine dispenses with each use. They have data that says at the medium setting the automated machine dispenses with a standard deviation of 17 ml. The manager wants to estimate the amount dispensed with a margin of error of 5ml. With a 95% confidence what minimum sample size should the fast food restaurant obtain.