Some geysers such as Old Faithful in Yellowstone National Park are remarkably consistent in the periodicity of their eruption. For example, in 1988, 6,900 timed intervals between eruptions for Old Faithful averaged 76.17 minutes, with the shortest observed interval 41 minutes and the longest 114 minutes. In the past 120 years Old Faithful's yearly average interval has always been between 60 and 79 minutes.

It is also well known that the relationship between the length of the eruption and the length of the subsequent interval duration is a positive one. Suppose the following data were collected over a several day period.

1: Compute r, the Pearson correlation coefficient

2: At the 0.05 level of significance, test the null hypothesis that the (“eruption time” and the “interval duration”) population correlation coefficient [ρ] is equal to 0.

3: Compute and use the regression equation you came up with in the previous part (namely “f”) to predict the “interval duration” for an “eruption time” of 6 minutes.

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 α = 0.05.

a) Find the value of the test statistic for method of loading and unloading.

Find the p-value for method of loading and unloading. (Round your answer to three decimal places.)

p-value =

b) Find the value of the test statistic for type of ride.

Find the p-value for type of ride. (Round your answer to three decimal places.)

p-value =

c) Find the value of the test statistic for interaction between method of loading and unloading and type of ride.

Find the p-value for interaction between method of loading and unloading and type of ride. (Round your answer to three decimal places.)

p-value =

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 contribute 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.

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

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

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

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

What is your conclusion with respect to Factor A?

- Select your answer -Factor A is significant Factor A is not significant Item 22

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

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 α = 0.05.

Find the p-value for method of loading and unloading. (Round your answer to three decimal places.)Find the value of the test statistic for method of loading and unloading.

p-value =

State your conclusion about method of loading and unloading.

Because the p-value ≤ α = 0.05, method of loading and unloading is significant.Because the p-value ≤ α = 0.05, method of loading and unloading is not significant.    Because the p-value > α = 0.05, method of loading and unloading is not significant.Because the p-value > α = 0.05, method of loading and unloading is significant.

Find the value of the test statistic for type of ride.

Find the p-value for type of ride. (Round your answer to three decimal places.)

p-value =

State your conclusion about type of ride.

Because the p-value ≤ α = 0.05, type of ride is significant.Because the p-value ≤ α = 0.05, type of ride is not significant.    

Because the p-value > α = 0.05, type of ride is not significant.Because the p-value > α = 0.05, type of ride is significant.

Find the value of the test statistic for interaction between method of loading and unloading and type of ride.

Find the p-value for interaction between method of loading and unloading and type of ride. (Round your answer to three decimal places.)

p-value =

State your conclusion about interaction between method of loading and unloading and type of ride.

Because the p-value > α = 0.05, interaction between method of loading and unloading and type of ride is significant.Because the p-value ≤ α = 0.05, interaction between method of loading and unloading and type of ride is significant.    

Because the p-value > α = 0.05, interaction between method of loading and unloading and type of ride is not significant.

Because the p-value ≤ α = 0.05, interaction between method of loading and unloading and type of ride is not significant.

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?