The correlation between the following two lists is zero, can you explain why? 1,2,3,4,5,6,7 7,6,5,4,5,6,7 Correlation of 1st half of the list is negative and between the last half of the list is positive so they cancel out The second list is totally random with respect to the first list, therefore they don't correlate at all

WAITING LINES

The Peachtree Airport in Atlanta serves light aircraft. It has a single runway and one air traffic controller to land planes. It takes an airplane 10 minutes to land and clear the runway, but planes arrive at the rate of 4 per hour.

Set up the waiting lines problem and be prepared to answer questions from the output

WAITINGLINES(Airport)

__________8a. What is the average number of planes that will stack up waiting to land?

__________8b. What is the average time a plane must wait in line before it can land?

__________8c. What is the probability that no planes are in the area and the traffic controller

can actually take a breather?
__________8d. What is the average time it takes a plane to clear the runway once it has notified

the airport that it is in the vicinity and wants to land?

__________8e. If the FAA requires 15 minutes of idle time every hour for their Air Traffic

Controllers (75% utilization), will the airport have to hire an extra one?

Consider the Fibonacci sequence 1,1,2,3,5,8,13,21,34,55,89,…. . The first two numbers are 1 and 1. When you add these numbers you get 2 = 1+1, which becomes the third number in the sequence. When you add the second and third numbers, you get 3 = 1+2, which becomes the fourth number in the sequence. When you add the third and fourth numbers, you get 5 = 2+3, which becomes the fifth number in the sequence; and so on to generate the sequence. Write a short Excel program that generates the first 50 numbers of the Fibonacci sequence, using 1 and 1 as the first two numbers to start the sequence. Put these numbers in Column A in Excel. Also, in the next column in Excel (Column B), divide each number in the sequence by the previous number in the sequence. This column is a new sequence of numbers. Start Column B in Row 2. To what number does the sequence of the quotients in Column B converge? Use the 2-D Bar Chart tool in Excel to graph the first 10 ratios in Column B

The Hickory Furniture Co. produces sofas and chairs. Their plant uses three main resources to make furniture –wood, upholstery and labor. The resource requirements and profits for each piece of furniture and the total resources available weekly are as follows:

LINEAR PROGRAMMING (Hickory Furniture)

__________ 1a. How many sofas should be produced?
__________ 1b. How many chairs should be produced?
__________ 1c. How much profit will be earned optimally?
__________ 1d. What is the value of an additional hour of labor to the total profit?
__________ 1e. How much would the profit increase with an additional yard of upholstery?

__________ 1f. How much of the 1200 lbs of wood are actually used in the optimal solution?

__________ 1g. What is the lowest profit for sofas that would have the same optimal solution?

__________ 1h. What is the highest profit for chairs that would have the same optimal solution?

I would like to know if the sex of a math student is a statistically significant factor in predicting average math exam scores. The following lists are exam scores for a math exam, separated by sex.

male 89 33 104 48 90 80 98 32 98 55 75 74 73 90 105 47 48 67 99 103 63

female 99 80 81 88 94 83 70 42 78 75

Perform a hypothesis test to determine whether the sex of a math student is statistically significant for performance on math tests. In other words, is there a statistically significant difference between the scores of these two groups of students?

(a) State the null and alternative hypotheses. Also, state the meaning of your parameters.

(b) Perform the test. Use α = .05. Show your work. Clearly indicate the value of the test statistic. Be sure to mention the value of df if it is relevant. Also, make sure you clearly state your final answer to the question above.

(c) Compute an appropriate 95% confidence interval that would confirm your final answer from part (b). Explain why it confirms that answer.

GRADED PROBLEM SET #8

Answer each of the following questions completely. When possible to answer using a complete sentence and offering explanation, please do so. There are a total of 20 points possible in the assignment.

1. Resveratrol, an ingredient in red wine and grapes, has been shown to promote weight loss in rodents. One study investigates whether the same phenomenon holds true in primates. The grey mouse lemur, a primate, demonstrates seasonal spontaneous obesity in preparation for winter, doubling its body mass. A sample of six lemurs had their resting metabolic rate, body mass gain, food intake, and locomotor activity measured for one week prior to resveratrol supplementation (to serve as a baseline) and then the four indicators were measured again after treatment with a resveratrol supplement for four weeks. Some p-values for tests comparing the mean differences in these variables are given below. In parts a-d, state the conclusion of the test using a 5% significance level, and interpret the conclusion in context. (HINT: For thinking of the null/alternative hypothesis, the null would be that there is no change and the alternative would be what they are trying to test as described in the wording in each part)
   1. In a test to see if mean resting metabolic rate is higher after treatment, p=0.013

2. In a test to see if mean body mass gain is lower after treatment, p=0.007

3. In a test to see if mean food intake is affected by the treatment, p=0.035

4. In a test to see if locomotor activity is affected by the treatment, p=0.980

5. In which test is the strongest evidence for rejecting the null found? The weakest?

6. How do your answers to parts a-d change if the researchers make their conclusions using a stricter 1% significance level?

2. There were 2430 Major League Baseball games played in 2009, and the home team won the game in 53% of the games. If we consider the games played in 2009 as a sample of all MLB games, test to see if there is evidence, at the 5% level, that the home team wins more than half the games. (Show all steps of the hypothesis test to receive points)

Case 1 Instruction (Accounting Application) Use the MS Excel tabular graphical methods of descriptive statistics to summarize the sample data in the data set named PelicanStores in Case 1 folder. The managerial report should contain summaries such as:

1. A frequency and relative frequency distributions for the methods of payment (different cards). (20%)

2. Mean, median, first quartile, third quartile, and sample standard deviation for net sales from regular customers. (20%)

3. Mean, median, first quartile, third quartile, and sample standard deviation for net sales from married female. (20%)

4. Apply the location method to calculate the 60th percentile manually of net sales for each method (card) of payment. Please indicate which card has the highest 60th percentile and show the process. (20%)

5. Apply Chebyshev’s Theorem to calculate the range (i.e. $ to $) of at least 75% of the net sales must fall within for the Proprietary Card payment. (20%) (Hint: What is the z-score for at least 75% of data range?)

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. Change the confidence level to 99% to find the 99% confidence interval for the SLEEP variable.

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.

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

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

6. 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? Mean ______________ Standard deviation ____________________ Predicted percentage ______________________________ Actual percentage _____________________________ Comparison ___________________________________________________ ______________________________________________________________

7. 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? Predicted percentage between 40 and 70 ______________________________ Actual percentage _____________________________________________ Predicted percentage more than 70 miles ________________________________ Actual percentage ___________________________________________ Comparison ____________________________________________________ _______________________________________________________________ Why? __________________________________________________________ ________________________________________________________________

Use the Central Limit Theorem to find the mean and standard error of the mean of the sampling distribution. Then sketch a graph of the sampling distribution. The mean price of photo printers on a website is ​$228 with a standard deviation of ​$61. Random samples of size 34 are drawn from this population and the mean of each sample is determined. What is the standard deviation of the distribution of sample means ? (Type an integer or decimal rounded to three decimal places as​ needed.)

A study of 800 homeowners in a certain area showed that the average value of the homes is $182,000 and the standard deviation is $15,000. Find the probability that the mean value of these homes is less than $185,000.

Round answer to 4 decimal places.

1) Using the tdist function, calculate exact p-values for a two tailed test for the following test statistics (6 points)

a) 2.14, df = 79 (2 points) b) 3.68, df = 13 (2 points) c) 1.78, df = 117 (2 points)

Based on data from a​ college, scores on a certain test are normally distributed with a mean of 1518 and a standard deviation of 324.

Standard score   Percent
-3.0   0.13
-2.5   0.62
-2   2.28
-1.5   6.68
-1   15.87
-0.9   18.41
-0.5   30.85
-0.1   46.02
0   50.00
0.10   53.98
0.5   69.15
0.9   81.59
1   84.13
1.5   93.32
2   97.72
2.5   99.38
3   99.87
3.5   99.98

Find the percentage of scores greater than

2166

Find the percentage of scores less than

1194

Find the percentage of scores between

870

and

1680.

4000 B.C   1850 B.C.   150 A.D.
131   129   128
138   134   138
125   136   138
129   137   139
132   137   141
135   130   142
132   136   136
134   138   145
140   134   137

The values in the table below are measured maximum breadths​ (in millimeters) of male skulls from different epochs. Changes in head shape over time suggest that interbreeding occurred with immigrant populations. Use a 0.05 significance level to test the claim that the different epochs all have the same mean.

Find the p value