We need to find the confidence interval for the SLEEP variable. To do this, we need to find the mean and standard deviation with the Week 1 spreadsheet. Then we can the Week 5 spreadsheet to find the confidence interval.

First, find the mean and standard deviation by copying the SLEEP variable and pasting it into the Week 1 spreadsheet. Write down the mean and the sample standard deviation as well as the count. Open the Week 5 spreadsheet and type in the values needed in the green cells at the top. The confidence interval is shown in the yellow cells as the lower limit and the upper limit.

1. Give and interpret the 95% confidence interval for the hours of sleep a student gets.
2. Give and interpret the 99% confidence interval for the hours of sleep a student gets
3. Compare the 95% and 99% confidence intervals for the hours of sleep a student gets. Explain the difference between these intervals and why this difference occurs.

In the Week 2 Lab, you found the mean and the standard deviation for the HEIGHT variable for both males and females. Use those values for follow these directions to calculate the numbers again.

(From Week 2 Lab: Calculate descriptive statistics for the variable Height by Gender. Click on Insert and then Pivot Table. Click in the top box and select all the data (including labels) from Height through Gender. Also click on “new worksheet” and then OK. On the right of the new sheet, click on Height and Gender, making sure that Gender is in the Rows box and Height is in the Values box.   Click on the down arrow next to Height in the Values box and select Value Field Settings. In the pop up box, click Average then OK. Write these down. Then click on the down arrow next to Height in the Values box again and select Value Field Settings. In the pop up box, click on StdDev then OK. Write these values down.)

You will also need the number of males and the number of females in the dataset. You can either use the same pivot table created above by selecting Count in the Value Field Settings, or you can actually count in the dataset.

Then use the Week 5 spreadsheet to calculate the following confidence intervals. The male confidence interval would be one calculation in the spreadsheet and the females would be a second calculation.

1. Give and interpret the 95% confidence intervals for males and females on the HEIGHT variable. Which is wider and why?

2. Give and interpret the 99% confidence intervals for males and females on the HEIGHT variable. Which is wider and why?

3. Find the mean and standard deviation of the DRIVE variable by copying that variable into the Week 1 spreadsheet. Use the Week 4 spreadsheet to determine the percentage of data points from that data set that we would expect to be less than 40. To find the actual percentage in the dataset, sort the DRIVE variable and count how many of the data points are less than 40 out of the total 35 data points. That is the actual percentage. How does this compare with your prediction?

4. What percentage of data would you predict would be between 40 and 70 and what percentage would you predict would be more than 70 miles? Use the Week 4 spreadsheet again to find the percentage of the data set we expect to have values between 40 and 70 as well as for more than 70. Now determine the percentage of data points in the dataset that fall within this range, using same strategy as above for counting data points in the data set. How do each of these compare with your prediction and why is there a difference?

Monte Carlo Simulation

Tully Tyres sells cheap imported tyres. The manager believes its profits are in decline. You have just been hired as an analyst by the manager of Tully Tyres to investigate the expected profit over the next 12 months based on current data.

•Monthly demand varies from 100 to 200 tyres – probabilities shown in the partial section of the spreadsheet below, but you have to insert formulas to ge the cumulative probability distribution which can be used in Excel with the VLOOKUP command.
•The average selling price per tyre follows a discrete uniform distribution ranging from $160 to $180 each. This means that it can take on equally likely integer values between $160 and $180 – more on this below.
•The average profit margin per tyre after covering variable costs follows a continuous uniform distribution between 20% and 30% of the selling price.
•Fixed costs per month are $2000.

(a)Using Excel set up a model to simulate the next 12 months to determine the expected average monthly profit for the year. You need to have loaded the Analysis Toolpak Add-In to your version of Excel. You must keep the data separate from the model. The model should show only formulas, no numbers whatsoever except for the month number.

You can use this partial template to guide you:

The first random number (RN 1) is to simulate monthly demands for tyres.
•The average selling price follows a discrete uniform distribution and can be determined by the function =RANDBETWEEN(160,180) in this case. But of course you will not enter (160,180) but the data cell references where they are recorded.
•The second random number (RN 2) is used to help simulate the profit margin.
•The average profit margin follows a continuous uniform distribution ranging between 20% and 30% and can be determined by the formula =0.2+(0.3-0.2)*the second random number (RN 2). Again you do not enter 0.2 and 0.3 but the data cell references where they are located. Note that if the random number is high, say 1, then 0.3-0.2 becomes 1 and when added to 0.2 it becomes 0.3. If the random number is low, say 0, then 0.3-0.2 becomes zero and the profit margin becomes 0.2.
•Add the 12 monthly profit figures and then find the average monthly profit.

Show the data and the model in two printouts: (1) the results, and (2) the formulas. Both printouts must show the grid (ie., row and column numbers) and be copied from Excel and pasted into Word. See Spreadsheet Advice in Interact Resources for guidance.

(b)Provide the average monthly profit to Tully Tyres over the 12-month period.

(c)You present your findings to the manager of Ajax Tyres. He thinks that with market forces he can increase the average selling price by $40 (ie from $200 to $220) without losing sales. However he does suggest that the profit margin would then increase from 22% to 32%.

He has suggested that you examine the effect of these changes and report the results to him. Change the data accordingly in your model to make the changes and paste the output in your Word answer then write a report to the manager explaining your conclusions with respect to his suggestions. Also mention any reservations you might have about the change in selling prices.

The report must be dated, addressed to the Manager and signed off by you.
(Word limit: No more than 150 words)

A poll found that 74% of a random sample of 1029 adults said that they believe in ghosts.

determine the margin of error

1.Let x be a random variable that represents the percentage of successful free throws a professional basketball player makes in a season. Let y be a random variable that represents the percentage of successful field goals a professional basketball player makes in a season. A random sample of n = 6 professional basketball players gave the following information.

x

86

70

80

76

70

67

y

57

43

46

50

50

41

Given that Se ≈ 4.075, a ≈ 16.319, b ≈ 0.435, and x bar≈ 74.833 , ∑x = 449, ∑y = 287, ∑x2 = 33,861, and ∑y2 = 13,895, find a 99% confidence interval for y when x = 72.

Select one:

a. between 25.3 and 66.8

b. between 25.6 and 66.6

c. between 25.8 and 66.3

d. between 27.0 and 65.1

e. between 24.9 and 67.2

2.Let x be a random variable that represents the percentage of successful free throws a professional basketball player makes in a season. Let y be a random variable that represents the percentage of successful field goals a professional basketball player makes in a season. A random sample of n = 6 professional basketball players gave the following information.

x

65

80

68

64

69

71

y

43

49

51

47

42

52

Given that Se ≈ 4.306, a ≈ 17.085, b ≈ 0.417, and x bar≈ 69.5 , ∑x = 417, ∑y = 284, ∑x2 = 29,147, and ∑y2 = 13,528, find a 98% confidence interval for y around 53.4 when x = 87.

Select one:

a. between 26.4 and 77.3

b. between 25.1 and 78.6

c. between 24.6 and 79.1

d. between 21.3 and 82.5

e. between 23.8 and 79.9

3.Let x be a random variable that represents the percentage of successful free throws a professional basketball player makes in a season. Let y be a random variable that represents the percentage of successful field goals a professional basketball player makes in a season. A random sample of n = 6 professional basketball players gave the following information.

x

81

65

78

87

70

81

y

46

48

54

51

44

51

Given that Se ≈ 3.668, a ≈ 16.331, b ≈ 0.436, and x bar≈ 77 , use a 5% level of significance to find the P-Value for the test that claims β is greater than zero.

Select one:

a. 0.1 <  P-Value < 0.2

b. 0.005 <  P-Value < 0.01

c. P-Value < 0.005

d. 0.2 <  P-Value < 0.25

e. P-Value > 0.25

Park Rangers in a Yellowstone National Park have determined that fawns less than 6 months old have a body weight that is approximately normally distributed with a mean µ = 26.1 kg and standard deviation σ = 4.2 kg. Let x be the weight of a fawn in kilograms. Complete each of the following steps for the word problems below:  Rewrite each of the following word problems into a probability expression, such as P(x>30).  Convert each of the probability expressions involving x into probability expressions involving z, using the information from the scenario.  Sketch a normal curve for each z probability expression with the appropriate probability area shaded.  Solve the problem.

1. What is the probability of selecting a fawn less than 6 months old in Yellowstone that weighs less than 25 kilograms?

2. What is the probability of selecting a fawn less than 6 months old in Yellowstone that weighs more than 19 kilograms?

3. What is the probability of selecting a fawn less than 6 months old in Yellowstone that weighs between 30 and 38 kilograms?

4. If a fawn less than 6 months old weighs 16 pounds, would you say that it is an unusually small animal? Explain and verify your answer mathematically.

5. What is the weight of a fawn less than 6 months old that corresponds with a 20% probability of being randomly selected? Explain and verify your answer mathematically.

1. How long does it take an ambulance to respond to a request for emergency medical aid? One of the goals of one study was to estimate the response time of ambulances using warning lights (Ho & Lindquist, 2001). They timed a total of 67 runs in a small rural county in Minnesota. They calculated the mean response time to be 8.51 minutes, with a standard deviation of 6.64 minutes. Calculate a 95% confidence interval for the mean for this set of data.

1. State the desired level of confidence.
2. Calculate the confidence interval and confidence limits.
   • (1) Calculate the standard error of the mean (s¯¯¯X).(sX¯).
   • (2) Calculate the degrees of freedom (df ) and identify the critical value of t.
   • (3) Calculate the confidence interval and confidence limits.
3. Draw a conclusion about the confidence interval.

a 95% confidence interval was constructed for N = 67 ambulance runs. Assuming the mean and standard deviation remained the same (¯¯¯X=8.51,s=6.64)…(X¯=8.51,s=6.64)…

1. What is the confidence interval for the mean for N = 125 ambulance runs rather than 67?
2. What is the confidence interval for the mean for N = 33 ambulance runs rather than 67?
3. How do these two confidence intervals compare with the 95% confidence interval of (6.89, 10.13) calculated in Exercise 8?

2. For each of the following situations, calculate a 95% confidence interval for the mean (σ known), beginning with the step, “Identify the critical value of z.”

1. ¯¯¯X=50.00,σ¯¯¯X=3.00

A researcher suspects the mean trough (the lowest dosage of medication required to see clinical improvement of symptoms) level for a medication used to treat arthritis is higher than was previously reported in other studies. If previous studies found the mean trough level of the population to be 3.7 micrograms/mL, and the researcher conducts a study among 93 newly diagnosed arthritis patients and finds the mean trough to be 6.1 micrograms/mL with a standard deviation of 1.2 micrograms/mL, the researcher’s hypothesis, for a level of significance of 1%, should resemble which of the following sets of hypothesis?

A bakery would like you to recommend how many loaves of its famous marble rye bread to bake at the beginning of the day. Each loaf costs the bakery ​$4.00 and can be sold for ​$5.00. Leftover loaves at the end of each day are donated to charity. Research has shown that the probabilities for demands of​ 25, 50, and 75 loaves are 30​%, 25​%, and 45​%, respectively. Make a recommendation for the bakery to bake​ 25, 50, or 75 loaves each morning. Find the expected monetary value when baking 25 loaves. EMVequals​$ nothing ​(Type an integer or a​ decimal.) Find the expected monetary value when baking 50 loaves. EMVequals​$ nothing ​(Type an integer or a​ decimal.) Find the expected monetary value when baking 75 loaves. EMVequals​$ nothing ​(Type an integer or a​ decimal.) Make a recommendation for the bakery to bake​ 25, 50, or 75 loaves each morning. The bakery should bake ▼ 25 50 75 loaves of bread every morning.

The mean income per year of employees who produce internal and external newsletters and magazines for corporations was reported to be $76300. These editors and designers work on corporate publications but not on marketing materials. As a result of poor economic conditions and oversupply, these corporate communications workers may be experiencing a decrease in salary. A random sample of 40 corporate communications workers revealed that x̄ = $73000. Conduct a hypothesis test to determine whether there is any evidence to suggest that the mean income per year of corporate communications workers has decreased. Assume that the population standard deviation is $6360. Please use the exact value (from R) for all critical values.

Test statistic = -3.2816

P-value = 0.0005160833

a. Calculate the appropriate 99% bound that is consistent with a one-sample z-test.

b. Interpret the bound calculated above.

c. If the employer also found a cheaper medical insurance that reduced the amount of money that the employees have to pay for health insurance by $1000 per year, in practical terms, are the employees really taking home less money than before? Please explain your answer.

d. Explain why parts the test statistic and p-value state the same thing as the calculated bound. That is, what in the first part is consistent with the second part.

Please attach R code:

Use library(nycflights13) a. plot histogram for distance where carrier is "FL". Print graph(s). b. plot Two box plots side by side for distance where carrier are "FL" and “US”. Print graph(s). c. plot two histograms and two box plots in one graph where carrier are "FL" and “US”, equal scale for each box plot pair. Print graph(s).

Ted Olson, director of the company Overnight Delivery, is worried because of the number of letters of first class that his company has lost. These letters are transported in airplanes and trucks, due to that, mister Olson has classified the lost letters during the last two years according to the transport in which the letters were lost. The data is as follows:

Mister Olson will investigate only one department, either aerial o ground department, but not both. He will open the investigation in the department which has the most number of lost letters per month, find:

23.- The expectation value of lost letters per month in truck.

24.- The expectation value of lost letters per month in airplane.

Consider a sample with data values of 27, 25, 20, 15, 30, 34, 28, and 25. Compute the 22nd, 27th, 59th, and 69th percentiles. If needed, round your answers to two decimal digits.

Robert Altoff is vice president of engineering for a manufacturer of household washing machines. As part of a new product development project, he wishes to determine the optimal length of time for the washing cycle. Included in the project is a study of the relationship between the detergent used (four brands) and the length of the washing cycle (18, 20, 22, or 24 minutes). In order to run the experiment, 32 standard household laundry loads (having equal amounts of dirt and the same total weights) are randomly assigned to the 16 detergent–washing cycle combinations. The results (in pounds of dirt removed) are shown below.

Complete an ANOVA table. Use the 0.05 significance level. (Do not round your intermediate calculations. Enter your SS, MS, p to 3 decimal places and F to 2 decimal places.)

Data from the Bureau of Labor Statistics’ Consumer Expenditure Survey (CE) show that annual expenditures for cellular phone services per consumer unit increased from $237 in 2001 to $634 in 2007. Let the standard deviation of annual cellular expenditure be $52 in 2001 and $207 in 2007.

For the following 2 groups, do a power analysis to determine the statistical power at the p=0.05 and p=0.01 levels. For the power analysis, seek power for a difference in means of 2.79. Repeat the statistical analysis using 95% and 99% confidence intervals.

[11.540 8.203 8.214 13.165 11.451 13.015 11.060 10.488 8.849 8.271]

[4.708 8.013 9.886 7.026 6.051 5.546 7.914 9.951 9.880 7.381]