1. The health of the bear population in Yellowstone National Park is monitored by periodic measurements taken from anesthetized bears. A sample of n = 54 bears has a mean weight of ¯x = 182.9 lb and standard deviation of s = 121.8 lb. 86

(a) Calculate and interpret a 95% confidence interval estimate of the population mean µ bear weight.

(b) Find the length of the confidence interval constructed in part (a).

2. Hemoglobin levels in 11-year-old boys are normally distributed with unknown mean µ and standard deviation = 1.2 g/dL.

(a) Determine the sample size n needed to estimate population mean hemoglobin level with 95% confidence so that the margin of error E = 0.5 g/dL?

(b) Determine the sample size n needed to estimate population mean hemoglobin level with margin of error E = 0.5 g/dL with 99% confidence?

3.  A hospital administrator wished to estimate the average number of days µ
required for treatment of patients between the ages of 25 and 34. A random
sample of n = 35 hospital patients between these ages produced a sample mean
x¯ = 5.4 days and sample standard deviation s = 3.1 days.
(a) Calculate and interpret a 95% confidence interval for the mean length of stay µ for the population of patients from which the sample was drawn.
(b) Determine the length of the interval from part (a).
(c) Calculate and interpret a 99% confidence interval for the mean length of stay µ for the population of patients from which the sample was drawn.
(d) Determine the length of the interval from part (c).
(e) Why is the interval obtained in part (c) wider than that obtained in part (a)?

Buckeye Creek Amusement Park is open from the beginning of May to the end of October. Buckeye Creek relies heavily on the sale of season passes. The sale of season passes brings in significant revenue prior to the park opening each season, and season pass holders con- tribute a substantial portion of the food, beverage, and novelty sales in the park. Greg Ross, director of marketing at Buckeye Creek, has been asked to develop a targeted marketing campaign to increase season pass sales. Greg has data for last season that show the number of season pass holders for each zip code within 50 miles of Buckeye Creek. he has also obtained the total population of each zip code from the U.S. Census bureau website. Greg thinks it may be possible to use regression analysis to predict the number of season pass holders in a zip code given the total population of a zip code. If this is possible, he could then conduct a direct mail campaign that would target zip codes that have fewer than the expected number of season pass holders. *I only need help with #5,6,7 thank you

Managerial Report

1. Compute descriptive statistics and construct a scatter diagram for the data. Discuss your findings.

2. Using simple linear regression, develop an estimated regression equation that could be used to predict the number of season pass holders in a zip code given the total population of the zip code.

3. Test for a significant relationship at the .05 level of significance.

4. Did the estimated regression equation provide a good fit?

5. Use residual analysis to determine whether the assumed regression model is appropriate.

6. Discuss if/how the estimated regression equation should be used to guide the marketing campaign.

7. What other data might be useful to predict the number of season pass holders in a zip code?

An amusement park studied methods for decreasing the waiting time (minutes) for rides by loading and unloading riders more efficiently. Two alternative loading/unloading methods have been proposed. To account for potential differences due to the type of ride and the possible interaction between the method of loading and unloading and the type of ride, a factorial experiment was designed. Use the following data to test for any significant effect due to the loading and unloading method, the type of ride, and interaction. Use . Factor A is method of loading and unloading; Factor B is the type of ride.

Set up the ANOVA table (to whole number, but -value to 2 decimals and  value to 1 decimal, if necessary).

The -value for Factor A is - Select your answer -less than .01between .01 and .025between .025 and .05between .05 and .10greater than .10Item 21

What is your conclusion with respect to Factor A?

- Select your answer -Factor A is significantFactor A is not significantItem 22

The -value for Factor B is - Select your answer -less than .01between .01 and .025between .025 and .05between .05 and .10greater than .10Item 23

What is your conclusion with respect to Factor B?

- Select your answer -Factor B is significantFactor B is not significantItem 24

The -value for the interaction of factors A and B is - Select your answer -less than .01between .01 and .025between .025 and .05between .05 and .10greater than .10Item 25

What is your conclusion with respect to the interaction of Factors A and B?

- Select your answer -The interaction of factors A and B is significantThe interaction of factors A and B is not significantItem 26

What is your recommendation to the amusement park?

- Select your answer -Use method 1; it has a lower sample mean waiting time and is the best methodWithhold judgment; take a larger sample before making a final decisionSince method is not a significant factor, use either loading and unloading methodItem 27

Suppose a carnival director in a certain city imposes a height limit on an amusement park ride called Terror Mountain, due to safety concerns. Patrons must be at least 4 feet tall to ride Terror Mountain. Suppose patrons’ heights in this city follow a Normal distribution with a mean of 4.5 feet and a standard deviation of 0.8 feet (patrons are mostly children). Make sure to show all of your work in this question. Show the distribution that your random variable follows; state the probability you are asked to calculate; show any tricks you use; show how you standardize, and state your found value from Table A4.

a) [5 marks] What is the probability that a randomly selected patron would be tall enough to ride Terror Mountain?

b) [5 marks] A group of 3 friends want to ride Terror Mountain. What is the probability that their mean height is greater than 4.5 feet?

c) [7 marks] Another group of 5 friends wants to ride Terror Mountain. What is the probability that their mean height is between 4 and 4.25 feet, inclusive?

An amusement park studied methods for decreasing the waiting time (minutes) for rides by loading and unloading riders more efficiently. Two alternative loading/unloading methods have been proposed. To account for potential differences due to the type of ride and the possible interaction between the method of loading and unloading and the type of ride, a factorial experiment was designed. Use the following data to test for any significant effect due to the loading and unloading method, the type of ride, and interaction. Use . Factor A is method of loading and unloading; Factor B is the type of ride.

Set up the ANOVA table (to whole number, but p-value to 2 decimals and F value to 1 decimal, if necessary).

Jorge was at the park playing with friends. He found a typical die with 6 sides on the ground. He took it home and rolled it 100 times and recorded the results (found in the table below). He wanted to see if the die was a 'fair die' or if it was weighted on one side so somone could cheat when playing games!

Is this a 'fair die' or has it been tampered with? Test at the α=0.05 level of significance.

Which would be correct hypotheses for this test?

H0:μ1=μ2

; H1:μ1≠μ2
H0:
The die is a fair die; H1:
The die has been tampered with
H0:p1=p2
; H1:p1≠p2
H0:
The die has been tampered with; H1:

The die is a fair die

Roll count:

Rolled   Count
1   1
2   5
3   4
4   6
5   9
6   75

Test Statistic:

Give the P-value:

Which is the correct result:

Reject the Null Hypothesis
Do not Reject the Null Hypothesis

Which would be the appropriate conclusion?

There is enough evidence to suggest that the die has been tampered with.
There is not enough evidence to suggest that the die has been tampered with.

Adjusted WACC. ​ Hollydale's is a clothing store in East Park. It paid an annual dividend of ​$1.20 last year to its shareholders and plans to increase the dividend annually at 3.0​%. It has 590 comma 000 shares outstanding. The shares currently sell for ​$17.37 per share. ​ Hollydale's has 11 comma 000 semiannual bonds outstanding with a coupon rate of 6​%, a maturity of 24 ​years, and a par value of ​$1 comma 000. The bonds are currently selling for ​$638.46 per bond. What is the adjusted WACC for​ Hollydale's if the corporate tax rate is 40​%?

A new roller coaster at an amusement park requires individuals to be at least​ 4' 8"

​(56 inches) tall to ride. It is estimated that the heights of​ 10-year-old boys are normally distributed with

mu equals μ=55.0 inches and sigma equals σ=4 inches.

a. What proportion of​ 10-year-old boys is tall enough to ride the​ coaster?

b. A smaller coaster has a height requirement of

50 inches to ride. What proportion of​ 10-year-old boys is tall enough to ride this​ coaster?

c. What proportion of​ 10-year-old boys is tall enough to ride the coaster in part b but not tall enough to ride the coaster in part​ a?

A pair of bumper cars in an amusement park ride collide elastically as one approaches the other directly from the rear, as seen in part (a) of the figure below. ((a) before collision, (b) after collision) One has a mass of m1 = 462 kg and the other m2 = 546 kg, owing to differences in passenger mass. If the lighter one approaches at v1 = 4.48 m/s and the other is moving at v2 = 3.63 m/s, calculate the velocity of the lighter car after the collision.

Calculate the velocity of the heavier car after the collision.

Calculate the change in momentum of the lighter car.

Calculate the change in momentum of the heavier car.

(a) Have you ever visited an amusement park and taken a ride on a parachute drop ride? These types of rides take the passengers to a great height, and then drop them in free fall. Before they hit the ground, the ride is slowed using a Lenz’s law mechanism thus avoiding certain death. For this discussion, first locate a photo of one of these rides (either one you’ve personally experienced or one you might like to try someday), and in your initial post, upload the photo and respond to the following:

• Explain how Lenz’s law applies to this situation.
• Why is the Lenz’s law mechanism ideal for such a use?
• What other mechanisms can be used to slow the descent? Compare and contrast these options with the Lenz’s law mechanism.

(b) As you have learned, an electromagnet is a magnet that is produced by electric current. Think about how electromagnets are used and what you have seen or heard of them being used for. In your initial discussion post, respond to the following:

• Which of the principles or laws discussed in this module explain how an electromagnet works?
• Describe in detail two modern applications of electromagnets. Do these electromagnets draw a large amount of current or a little? How do you know? What supplies that current?
• Why do you think electromagnets are used in these different ways?
• What is the advantage of using an electromagnet rather than a permanent magnet?