Running times (Y) and maximal aerobic capacity (X) for 14 female
Runners. Data collected for running times and maximal aerobic capacity are listed below

X: 61.32 55.29 52.83 57.94 53.31 51.32 52.18 52.37 57.91 53.93 47.88 47.41 47.17 51.05

Y: 39.37 39.80 40.03 41.32 42.03 42.37 43.93 44.90 44.90 45.12 45.60 46.03      47.83 48.55

(a) Calculate the mean, median, MAD, MSD, and standard deviation for each variable. ? [Include all your steps and explain all the steps involved in details]
(b) Which of these statistics give a measure of the center of data and which give a measure of the spread of data?
(c) Calculate the correlation of the two variables and pro-duce a scatterplot of Y against X. [Use excel for scatterplot, show all your computations concerning the correlation and explain all your steps]
(d) Why is it inappropriate to calculate the autocorrelation of these data?

Econ 2310

Business Statistics: Problem Set #1

Instructions: You may use Excel and/or a calculator to complete this assignment. Please show work or reference what Excel commands you used to solve the problems.

1. You are given the following two series on income and credit scores.

1. Find the covariance and the correlation coefficient. (B) Do credit scores increase, decrease, stay the same, with Income? (C) Create a scatter plot with Income and credit score. What do you see?

2. Suppose you flip a fair coin four time. (A) What is the probability you will get all four heads? (B) All four tails? (C) Either all four heads or four tails? (D) Anything but four heads or four tails?

3. Crime and Punishment: In a study of pleas and prison sentences, it is found that 45% of the subjects studied were sent to prison. Among those sent to prison, 40% chose to plead guilty. Among those not sent to prison, 55% chose to plead guilty.    

1. If one of the study subjects is randomly selected, find the probability of getting someone who was not sent to prison.
2. If a study subject is randomly selected and it is then found that the subject entered a guilty plea, find the probability that this person was not sent to prison.

4. In the BS Lottery (which stands for “Business Statistics”, of course), players choose 5 numbers out of 30. They win if they choose the same 5 numbers as our machine, which selects the numbers randomly. (A) How many permutations are possible? (B) How many combinations are possible?

5. Below is a table of X and its frequency. What is the mean of X? What is the standard deviation of X? What is the variance of X?

A coin that lands on heads with a probability of p is tossed multiple times. Each toss is independent. X is the number of heads in the first m tosses and Y is the number of heads in the first n tosses. m and n are fixed integers where 0 < m < n. Find the joint distribution of X and Y.

The manufacturers of Good-O use two different types of machines to fill their 25 kg packs of dried dog food. On the basis of random samples of size 15 and 18 from output from machines 1 and 2 respectively, the mean and standard deviation of the weight of the packs of dog food produced were found to be 26.856 kg and 0.218 kg for machine 1 and 24.818 kg and 0.369 kg for machine 2. Hence, under the usual assumptions, determine a 95% confidence interval for the difference between the average weight of the output of machine 1 and machine 2. Use machine 1 minus machine 2, stating the upper limit of the interval correct to three decimal places.

Define.

(a) Descriptive statistics

(b)Inferential Statistics

(c)Nominal Data

(d) Ordinal data

(e)Standard deviation

Brandon wants to find a cheap computer, but he knows that computer prices are extremely skewed, since most computers are very expensive. He knows that computer prices have a mean of $1,223 with a standard deviation of $1,214. Brandon finds the average price of 9 random computers. What is the probability the average price will be more than $1,688?
Use 4 decimal places.
Type in "cannot do" if that is your answer.

Identify if population parament or sample statistic:

Is statement population parameter or sample statistic? If, parameter, then identify population and parameter. If sample, then, what is population, sample, and statistic?

A) North Carolina State’s rugby team scored an average of 29.8 points per game in the 2015 season.

B) Based on a new poll of 5000 citizens, they believe that 89% of voters plan to cast their ballot for Mayor Green in the upcoming election.

C) A calculating fanatic conducts an experiment using 46 secretaries to see if there was an increase in typing speed and efficiency when changing from the QWERTY keyboard to the Dvorak keyboard. He found that the participants could type an average of 22.5 words per minute faster using the Dvorak keyboard.

D) A small business owner looks at his records from the past five years and determines that the average monthly cost of running his business is $5900.

2. Following, what level of measurement is used to measure variable? Identify if quantitative or categorical? If quantitative, identify if it is discrete or continuous?

A) How many cars have the persons owned over their lifetime?

B) Is the person dent right or left-handed?

C) What is the person's year of birth?

D) On a scale from 1 to 5, for 1 being not at satisfied and 5 being completely satisfied with the food, to what extent do you agree with the following statement – “I love math!”?

Statistics questions

In a Doctor’s office, the average wait time before a patient sees the doctor is normally distributed with mean 20minutes. Because of some actions taken at the office, the standard deviation has now reduced by 1 minute so, the standard deviation is now 2

7. Approximately 95% of the patients will now see a doctor between _______ and _________minutes

8. How unusual it is now to wait to be seen by the doctor for 30mins or more? _______% of patients wait beyond 30mins to be seen by a doctor.

9. 5% of the patients will now wait beyond______minutes

10. 10% of the (lucky!) patients will now be seen faster than how ________minutes

11. _______% of the patients wait more than 20mins to be seen by the doctor

A process has mean 11 and standard deviation 2.5. The process is monitored by taking samples of size 5 at regular intervals. The process is declared to be out of control if a point plots outside the 3σ control limits on a chart.

17a.) If the process mean shifts to 14, what is the average number of samples that will be drawn before the shift is detected on a X⎯⎯⎯X¯ chart?

17b.) An upward shift to what value will be detected with an ARL of 4?

17c.) If the sample size remains at 5, to what value must the standard deviation be reduced to produce an ARL of 4 when the process mean shifts to 14?

17d.) If the standard deviation remains at 2.5, what sample size must be used to produce an ARL of no greater than 4 when the process mean shifts to 14? Round up the answer to the nearest integer.

Suppose it is known that the IQ scores of a certain population of adults are approxi- mately normally distributed with a standard deviation of 15. A simple random sample of 25 adults drawn from this population had a mean IQ score of 105.

a) Is there evidence at 5% significance level that the average IQ in this population is not equal to 100?

Please also explain how you got the critical value.

Thanks!!!

1. Given: A 4-inch cube with all 6 faces painted is cut up into 64 1-inch cubes. A cube is picked at random. What is the probability that (a) It is unpainted: ________________________________ (b) It has at most 1 face painted: _________________________

In 2011, when the Gallup organization polled investors, 34% rated gold the best long-term investment. In April of 2013 Gallup surveyed a random sample of U.S. adults. Respondents were asked to select the best long-term investment from a list of possibilities. Only 241 of the 1005 respondents chose gold as the best long-term investment. By contrast, only 91 chose bonds.

1. Compute the standard error for each sample proportion. Compute and describe a 95% confidence interval in the context of the question.
2. Do you think opinions about the value of gold as a long-term investment have really changed from the old 34% favorability rate, or do you think this is just sample variability? Explain.
3. Suppose we want to increase the margin of error to 3%, what is the necessary sample size?
4. Based on the sample size obtained in part c, suppose 120 respondents chose gold as the best long-term investment. Compute the standard error for choosing gold as the best long-term investment. Compute and describe a 95% confidence interval in the context of the question.
5. Based on the results of part d, do you think opinions about the value of gold as a long-term investment have really changed from the old 34% favorability rate, or do you think this is just sample variability? Explain.

(Please show calculations especially if formatted via excel)

Suppose that the antenna lengths of woodlice are approximately normally distributed with a mean of 0.2 inches and a standard deviation of 0.05 inches. What proportion of woodlice have antenna lengths that are less than 0.23 inches? Round your answer to at least four decimal places.

Can you tell me the step by step process of how to do this?

Provide a substantive response that addresses all areas of the item below. Your organization has asked you to estimate the proportion of current employees who expect to retire by the age of 65. Develop an appropriate sampling frame and sampling approach to facilitate this task. Note: Your sample must be random. Outline the data collection process you would employ. Additionally, provide a substantive response to the following questions:

I chose my company to have 500 employees and a sampling frame of 21.

(Employee #1- 132, #2 - 223, 3 - 455, #4 - 63, #5 - 447, #6- 324, #7-320, #8 - 333 #9 - 258, #10 - 263, #11- 34, #12 - 137, #13 - 226, #14 - 353, #15 - 59, #16 - 24, #17 - 261, #18 - 424, #19 - 146, #20 - 28 #21 - 62.

Q1. Is using 21 employees for a sampling frame appropriate number for a population of 500? Was I suppose to use a formula to get the sampling frame or was my preference acceptable?

Q2. Do I randomly select the number for employees out of the 500 or is that a formula that needs to be calculated?

Q3. What considerations need to be made when defining and collecting information from a sample?

Q4. What problems might you encounter and how frequently might they occur? Please advise