StatisticsDocumentsSUMA11 Final exam solution  $4.00
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4  4
(a) Find the mean, median, mode, sample variance, and range. (b) Do you think that this sample might have come from a normal population? Why or why not? Homework set Review  $6.00
Price 6.00 USD 1. A student organization is interested to find the percentage of the students that smoke, in a local university. A random sample of size 100 students (N=12000) were selected. The respondents were asked whether they smoke? 30 responded yes and the rest said no. a. Specify the population. b. What is the parameter of this population? c. What is the relevant sample statistic in this problem? d. What is the best estimate of the percentage of students that smoke? e. How can the student organization improve the answer to part “d”? 2. Identify the following variables as qualitative or quantitative. a. Gender b. Salary c. Class designation d. Education level e. Sales f. Temperature g. Make of a car h. Height i. Season of the year j. Advertising expenditure k. Type of advertising l. Store location 3. The grades of a student in five subjects are: 85, 92, 81, 70, 92. a. Find the mean grade. b. Find the range of grade. c. Find the variance and standard deviation using Excel’s functions. d. Find the variance and standard deviation using Excel’s “Descriptive Statistics” feature. e. Are the answers in parts “c” and “d” equal? 4. The diameters of a sample of rods delivered are 0.99, 1.02, 1.04, 0.98, 0.97. Using Excel Create a table with the following columns: a. Enter the above data in the first column. b. Calculate the mean. c. Calculate the difference between each observation and the mean. Is the sum of this column equal zero? If not, double check your calculations. d. In the next column, square each of the deviations around the mean. Divide the total of this column by (n1) degrees of freedom. Is your answer the same as the sample variance you found in the previous problem? 5. The number of service calls received by a local fire department is between 0 and 5. The probabilities are .10, .15, .30, .20, .15, .10, respectively. a. Write the probability distribution for the number of service calls in a given day. b. What is the expected number of service calls per day in this fire department? 6. Consider the example of flipping a coin two times. a. List all possible outcomes of this experiment. b. Assume we are interested in the number of heads facing up after the flipping the coin twice. What is the random variable of interest? c. Is the random variable of interest discrete or continuous? d. Show the probability distribution of this random variable. 7. It is known that the average weekly rate of that the distribution of wage is normal with a standard deviation of $100. a. What is the median weekly wage rate? b. What is the probability that a production worker earn between $500 and $800? c. What is the probability that a production worker earn more than $800? d. What percent of production workers earn more than $1000 per week? e. What is the probability that a sample of size 50 workers has an average weekly salary of more than $700. 8. Assuming that the price of gas per gallon in a city is normally distributed with a mean of $1.90 and a standard deviation of $0.10, answer the following questions: a. What percent of gas stations charge within ± 10¢, 20¢, and 30¢ around the mean? b. Find two prices symmetrically around the mean in which 90% of gas stations charge within those two prices.. c. Find two prices symmetrically around the mean in which 95% of gas stations charge within those two prices. d. Find two prices symmetrically around the mean in which 99% of gas stations charge within those two prices. e. What is the probability a gas station selected at random charge more than $2.50. 9. A bottling company sets a machine to fill 12 ounces of a soft drink in every bottle. A State inspector, in looking out for customers, selects a random sample of 49 bottles once a week. If the mean of the sample is less than 11.98 ounces, the company is given a $1000 fine. Assume that the population standard deviation is 0.07 ounces. a. Find the mean and standard deviation of the distribution of the mean of the samples selected by the inspector. b. What is the shape of the distribution of c. Find the probability that the mean of an inspector’s sample is less than 11.98 ounces. d. Find the probability that a bottle selected at random has less than 11.98 ounces of the soft drink. 10. The population average for SAT score is 1020, with a population standard deviation of 100. a. What is the standard deviation of the distribution of b. What is the probability that a random sample of 64 students will provide a sample mean SAT score within 10 points of the population mean? 11. A a. What is the point estimation for the mean of the population? b. At 90% level of confidence, what is the margin of error? c. What is the 90% confidence level for the mean of the population? 12. A car rental company is interested to estimate the average miles its cars are driven in a particular holiday. A sample of 200 cars is selected from its fleet of 25000 cars. The mean and standard deviation of the sample are 54.50 and 14 miles, respectively. a. Develop a 95% confidence interval for the average miles driven. b. In another region 200 cars were rented and $2500 of fees was collected. Given that 25 cents are charged per miles driven, is there any reason to investigate the billing practices in the other region? Support your answer using the confidence interval in part “a”. Support your answer using statistical reasoning and logic. 13. A sample of 8 senior citizens indicate the following prescription cost in dollar for Zocor (a drug used to lower the cholesterol): 98 104 126 110 112 115 100 99 a. What is the point estimate for the population mean of the prescription cost of Zocor? b. Assuming that the distribution of Zocor prescription cost is normally distributed, find the 95% confidence interval estimate for the population mean prescription cost of Zocor? 14. A Cell Phone company sells cellular phones and airtime in a State. At a recent meeting, the marketing manager states that the average age of the customers is 40 years. Before actually completing the advertising plan, it was decided to select a random sample of customers. Among the questions asked in the survey of 50 customers was the customer’s ages. The mean and the standard deviation of the data based on the survey are 38 years and 7 years. a. Formulate a hypothesis to test the marketing manager’s claim. b. Does the sample support manager’s claim. Test at 0.05 level of significance. 15. A manufacturer claims that one of its new cars having a highway fuel efficiency average of 30 miles per gallon (MPG). A consumer interest group would like to test whether there is any statistical evidence that the manufacturer is over stating the MPG. A sample of 25 cars of this brand resulted in a sample mean highway mileage rating of 29.5 MPG and a standard deviation of 1.8 MPG. a. State the null and alternative hypotheses needed to conduct this test? b. What test statistic should be used and why? Should any assumption be made about the distribution of MPG? c. What conclusion can be drawn from the sample results? Test at 0.05 level of significance. Week 4 iLab solution Suma 11  $4.00
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Ø Open a new MINITAB worksheet. Ø We are interested in a binomial experiment with 10 trials. First, we will make the probability of a success ¼. Use MINITAB to calculate the probabilities for this distribution. In column C1 enter the word ‘success’ as the variable name (in the shaded cell above row 1. Now in that same column, enter the numbers zero through ten to represent all possibilities for the number of successes. These numbers will end up in rows 1 through 11 in that first column. In column C2 enter the words ‘one fourth’ as the variable name. Pull up Calc > Probability Distributions > Binomial and select the radio button that corresponds to Probability. Enter 10 for the Number of trials: and enter 0.25 for the Event probability:. For the Input column: select ‘success’ and for the Optional storage: select ‘one fourth’. Click the button OK and the probabilities will be displayed in the Worksheet. Ø Now we will change the probability of a success to ½. In column C3 enter the words ‘one half’ as the variable name. Use similar steps to that given above in order to calculate the probabilities for this column. The only difference is in Event probability: use 0.5. Ø Finally, we will change the probability of a success to ¾. In column C4 enter the words ‘three fourths’ as the variable name. Again, use similar steps to that given above in order to calculate the probabilities for this column.The only difference is in Event probability: use 0.75. Plotting the Binomial Probabilities 1. Create plots for the three binomial distributions above. Select Graph > Scatter Plot and Simple then for graph 1 set Y equal to ‘one fourth’ and X to ‘success’ by clicking on the variable name and using the “select” button below the list of variables. Do this two more times and for graph 2 set Y equal to ‘one half’ and X to ‘success’, and for graph 3 set Y equal to ‘three fourths’ and X to ‘success’. Paste those three scatter plots below. Calculating Descriptive Statistics Ø Open the class survey results that were entered into the MINITAB worksheet.
2. Calculate descriptive statistics for the variable where students flipped a coin 10 times. Pull up Stat > Basic Statistics > Display Descriptive Statistics and set Variables: to the coin. The output will show up in your Session Window.Type the mean and the standard deviation here. Short Answer Writing Assignment – Both the calculated binomial probabilities and the descriptive statistics from the class database will be used to answer the following questions. 3. List the probability value for each possibility in the binomial experiment that was calculated in MINITAB with the probability of a success being ½. (Complete sentence not necessary) 4. Give the probability for the following based on the MINITAB calculations with the probability of a success being ½. (Complete sentence not necessary) 5. Calculate the mean and standard deviation (by hand) for the MINITAB created binomial distribution with the probability of a success being ½. Either show work or explain how your answer was calculated. Mean = np, Standard Deviation = 6. Calculate the mean and standard deviation (by hand) for the MINITAB created binomial distribution with the probability of a success being ¼ and compare to the results from question 5.Mean = np, Standard Deviation = 7. Calculate the mean and standard deviation (by hand) for the MINITAB created binomial distribution with the probability of a success being ¾ and compare to the results from question 6.Mean = np, Standard Deviation = 8. Explain why the coin variable from the class survey represents a binomial distribution.
9. Give the mean and standard deviation for the
coin variable and compare these to the mean and standard deviation for the
binomial distribution that was calculated in question 5. Explain how they are
related.Mean = np, Standard Deviation Stats questions  $5.00
Price 5.00 USD BASEBALL DATA: 1. Refer to the Baseball 2009 data, which reports information on the 30 Major League Baseball teams for the 2009 season. Select an appropriate class interval and organize the team salaries into a frequency distribution. a. What is a typical team salary? What is the range of salaries? b. Comment on the shape of the distribution. Does it appear that any of the team salaries are out of line with the others? c. Draw a cumulative frequency distribution. Forty percent of the teams are paying less than what amount in total team salary? About how many teams have total salaries of less than $80,000,000? BUENA SCHOOL DATA 2. Refer to the Buena School District bus data. Prepare a report on the maintenance cost for last month. Be sure to answer the following questions in your report. a. Around what values do the data tend to cluster? Specifically what was the mean maintenance cost last month? What is the median cost? Is one measure more representative of the typical cost than the others? b. What is the range of maintenance costs? What is the standard deviation? About 95 percent of the maintenance costs are between what two values? REAL ESTATE DATA: 3. Refer to the Real Estate data, which reports information on homes sold in the Goodyear, Arizona, area during the last year. Prepare a report on the selling prices of the homes. Be sure to answer the following questions in your report. a. Develop a box plot. Estimate the first and the third quartiles. Are there any outliers? b. Develop a scatter diagram with price on the vertical axis and the size of the home on the horizontal. Does there seem to be a relationship between these variables? Is the relationship direct or inverse? c. Develop a scatter diagram with price on the vertical axis and distance from the center of the city on the horizontal axis. Does there seem to be a relationship between these variables? Is the relationship direct or inverse? 4. Refer to the Real Estate data, which reports information on homes sold in the Goodyear, Arizona, area during the last year. a. Sort the data into a table that shows the number of homes that have a pool versus the number that don't have a pool in each of the five townships. If a home is selected at random, compute the following probabilities. 1. The home is in Township 1 or has a pool. 2. Given that it is in Township 3, that it has a pool. 3. The home has a pool and is in Township 3. b. Sort the data into a table that shows the number of homes that have a garage attached versus those that don't in each of the five townships. If a home is selected at random, compute the following probabilities: 1. The home has a garage attached. 2. The home does not have a garage attached, given that it is in Township 5. 3. The home has a garage attached and is in Township 3. 4. The home does not have a garage attached or is in Township 2. 5. Refer to the Real Estate data, which report information on homes sold in the Goodyear, Arizona, area last year. a. Create a probability distribution for the number of bedrooms. Compute the mean and the standard deviation of this distribution. b. Create a probability distribution for the number of bathrooms. Compute the mean and the standard deviation of this distribution. 6. Refer to the Real Estate data, which report information on homes sold in the Goodyear, Arizona, area during the last year. a. The mean selling price (in $ thousands) of the homes was computed earlier to be $221.10, with a standard deviation of $47.11. Use the normal distribution to estimate the percentage of homes selling for more than $280.0. Compare this to the actual results. Does the normal distribution yield a good approximation of the actual results? b. The mean distance from the center of the city is 14.629 miles, with a standard deviation of 4.874 miles. Use the normal distribution to estimate the number of homes 18 or more miles but less than 22 miles from the center of the city. Compare this to the actual results. Does the normal distribution yield a good approximation of the actual results? QM203  HW ASSIGNMENTS  $5.00
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QM203  HW ASSIGNMENTS
HW Set #3  Ch 11 – Regression Analysis – Statistical Inference (Read All) ______________________________________________________________________________
The relevant data for some of the problems in this HW set may be found in the HW Set # 2.
I. Oil Problem Continued – A small sample data is collected for two variables. Y represents the price of all gas types per gallon (Bureau of Labor Statistics data), and X represents the average price of crude oil per barrel (Department of energy data), for a period of ten years. Based on the summary output of the fitted linear model you developed in HW Set #2, answer the following questions.
1. Is the linear model useful for the prediction of price of gas? Test using α =0.05. Use critical value approach. 2. Is the linear model useful for the prediction of price of gas? Test using α =0.05. Use pvalue approach. 3. Conduct an F test (Critical value approach) to test the usefulness of the model. Use α =0.05. 4. Conduct an F test (pvalue approach) to test the usefulness of the model. Use α =0.05. 5. Did you come up with the same conclusion in all previous parts? Is it possible to get conflicting answers? Explain. 6. Develop a 95% confidence interval for the slope of the model. Interpret the meaning of the interval in the context of the problem. 7. Develop a 90% confidence interval for the slope of the model. Compare it to the answer you got in the precious part. Which interval is wider? Does it make sense? Explain.
II. Corvette Problem Continued  A random sample of ten used cars (Corvettes) between 1 and 6 years old were selected from a used car dealership. The relevant data (see HW Set #2) were obtained. x represents age, in years, and y represents sales price, in hundreds of dollars.
1. Obtain the residuals and create a residual plot. Identify outliers and influential observations. 2. Are any of the regression assumptions violated? Explain. 3. At 5% level of significance, do data provide sufficient evidence to conclude that the slope of the population regression line is not zero and, thus, the variable age is useful for prediction of price for Corvettes? 4. Based on the summary output, report the 95% confidence interval for the slope, β_{1}, of the population. Interpret the results. 5. Using the fitted model, predict the price of a corvette that is 5 years old. 6. Find a 95% prediction interval for sales for a corvette that is 5 years old.
III. The Quality Problem Continued  The Quality of a product depends on temperature and Pressure (in PSI). Using 27 observations (see HW Set # 2), the following models were fitted to the data. Firstorder model Interaction model Complete secondorder model
Answer the following questions: 1. At α= 0.05, test whether the complete secondorder model significantly contribute to the prediction of Quality? 2. Is the complete secondorder model preferable to the interaction model? Test using α= 0.05. 3. Is the complete secondorder model preferable to the firstorder model? Test using α= 0.05. 4. Predict the quality of s product at 50 PSI and 100 degrees of temperature. 5. Develop a 95% prediction interval when PSI is 50 and temperature is 100 degrees. Use a statistical software such as StatTools to answer this question.
IV. A Chain Of Clothing Stores Problem Continued  wants to develop a model that can predict sales based the store’s location. Data of this problem may be found in the HW Set # 2. The following model is proposed, and fitted to the data. Using the regression summary output, answer the following questions. 1. Is there any difference in sales between location 4 and 1? Test using α= 0.05. 2. Do sales depend on the location where the store is located? Test using α= 0.05.
V. A Fast Food Problem Continued  is interested in modeling the mean weekly sales of a restaurant, E(y), as a function of the weekly traffic flow on the street where the restaurant is located and the city in which the restaurant is located. The table contains data that were located on 24 restaurants in four cities is give in HW Set #2. Two models are already fitted to the data.
where
1. In model 1, at , test the null hypothesis that . Interpret the results of your test. 2. In model 1, is the mean weekly sales, E(y), dependent on the city where a restaurant is located? Test using Interpret the results of your test. 3. Do the data provide sufficient evidence to indicate that the slopes of the lines differ for at least two of the four cities? Test using (Hint: All of the parameters of the model that make the slopes of the lines differ, must be tested.)
Multiple Choice Questions:
1. In multiple regression analysis, the correlation among the independent variables is termed a. homoscedasticity b. linearity c. multicollinearity d. adjusted coefficient of determination 2. In a multiple regression model, the error term e is assumed to a. have a mean of 1 b. have a variance of zero c. have a standard deviation of 1 d. be normally distributed 3. In order to test for the significance of a regression model involving 14 independent variables and 50 observations, the numerator and denominator degrees of freedom (respectively) for the critical value of F are a. 13 and 48 b. 13 and 49 c. 14 and 48 d. 14 and 35 e. none of the above 4. A multiple regression analysis includes 4 independent variables results in sum of squares for regression of 1400 and sum of squares for error of 600. The multiple coefficient of determination will be: a. 0.300 b. 0.700 c. 0.429 d. 0.084 e. none of the above 5. A multiple regression analysis includes 4 independent variables results in sum of squares for regression of 2800 and sum of squares for error of 1200. If the sample size is 20, the standard error of estimate will be: a. 8.00 b. 80.00 c. 140.62 d. 8.94 e. none of the above 6. There are situations where a set of explanatory variables forms a logical group. The test to determine whether the extra variables provide enough extra explanatory power to warrant inclusion in the equation is the: a. complete Ftest b. reduced Ftest c. partial Ftest d. reduced ttest e. none of the above 7. In the example of explaining a person’s height by means of his/her right and left foot length, how would you treat for multicollinearity? a. Eliminate the right foot variable b. Eliminate the left foot variable c. Eliminate either foot variable d. Eliminate both feet variables e. None of the above 8. Determining which variables to include in regression analysis by estimating a series of regression equations by successively adding or deleting variables according to prescribed rules is referred to as: a. elimination regression b. logical regression c. forward regression d. backward regression e. stepwise regression
Figure 1. A sample of 16 cars is selected. The data related to price (in $1000s), horsepower, and speed at 1/4 mile (MPH), is collected. The summary output for the model that predicts speed at ¼ mile based on the price and horsepower is given below.
Using Figure 1 above, answer the following questions:
9. To test whether Price significantly contributes to the prediction of MPH, what is the value of the test statistic we should use, is a. 33.0252 b. 2.7638 c. 9.2896 d. 77.4007
10. To test whether Price significantly contributes to the prediction of MPH, what is the pvalue we should use? You may also use “=tdist(statistic,df,2)”. a. <0.0000 b. 0.0161 c. <0.0001 d. 0.2113
11. To test whether the model significantly contributes to the prediction of MPH, the value of the test statistic we should use, is a. 33.0252 b. 2.7638 c. 9.2896 d. 77.4007
12. To test whether the model significantly contributes to the prediction of MPH, what is the pvalue we should use? Hint: use “=fdist(statistic,df1,df2)” a. <0.0001 b. 0.0161 c. 0.5.433 d. 0.2113
13. Based on the above residual plot is there any outlier? a. No outlier present b. One outlier present c. Two outliers present d. More than 3 outliers present
14. Based on the above residual plot there is(are) only a. one observation beyond three standard errors b. two observations beyond three standard errors c. three observations beyond three standard errors d. none of the above
15. Based on the above summary output and the residual plot, we can say that a. there is (are) sign(s) for the existence multicollinearity b. the assumption of independence of error is violated c. the assumption of normality of error is violated d, none of the above _______________ 
