Miniprojects
Miniproject 7.3
Miniproject 7.7
For this project, select a football league of your choice (in your country or a European one). Obtain data on the heights and ages of all players in a given year.
For this project use either the ADCB Trading file or the Kuwait Stock Market file. Define a random variable as (Close Price – Open Price) for ADCB and (Close Market Index – Open Market Index) for the Kuwait Stock Market. The difference will be positive if an in crease occurs, zero if there is no change, or negative if a decrease occurs. Take a sample (using random numbers) of 35 values of the random variable.
a) Take a random sample of 20 players and find a 95% confidence interval for , the popula tion mean age. Assume that the ages of these players are normally distributed. b) Redo part a) for samples of size 30 and 50 respectively. c) Compare the widths of these three confi dence intervals. d) Compute the mean of the population of ages of all players. Which confidence intervals contain ?
Miniproject 7.4 Use the data you obtained for Miniproject 7.3. Take 15 random samples of 20 players. a) Compute a 95% confidence interval for the proportion of players who scored five goals during the season for each sample. b) Compute the population proportion p of all players who scored five goals during the season. c) What percentage of confidence intervals con tain the population proportion p computed in b)? d) Is this percentage close to the confidence level of 95%?
Miniproject 7.5 Use the data file Brazilian Football Players. Select the variables height and age of players. a) Take a random sample of 20 players and find a 95% confidence interval for , the popula tion mean age. Assume that the ages of these players are normally distributed. b) Redo part a) for samples of size 30 and 50 respectively. c) Compare the widths of these three confi dence intervals. d) Compute the mean of the population of ages of all players. Which confidence intervals contain ?
Miniproject 7.6 se the data file Brazilian Football Players. U Take 15 random samples of 20 players. Select the variable that indicates which foot a player prefers to use: left or right. a) Compute a 95% confidence interval for the proportion of players who are left-footed for each sample. b) Compute the population proportion p of all players who are left-footed. c) What percentage of confidence intervals contain the population proportion p com puted in b)? d) Is this percentage close to the confidence level of 95%?
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a) Find a 95% confidence interval for . b) Find a 90% confidence interval for s. c) What is the number of observations that you must collect if you want to be 95% confident that your error of estimation does not exceed 0.02 for ADCB or 17 for the Kuwaiti Stock Market. What assumption did you make? d) Define a new random variable: increase or decrease (disregard no change); let p be the proportion of increases. Find a 90% confi dence interval for this proportion.
Miniproject 7.8 For this project, you need to interview at least 50 customers doing their weekly shopping in a large su permarket. To conduct these interviews, form a team of three or four students. Prepare a questionnaire about weekly spending on groceries that contains a list of questions (no more than six, so that your interview will not take more than three minutes). Among the ques tions ask the following:
• Does this shopping correspond to your weekly budget for groceries? • If yes, what is the amount of the budget. • What is the size of the family you are shopping for? • What is the family income? (Do not insist if the customer does not want to answer.)
The data collected may be used for future mini projects; hence it is important that you execute this task well! Note that you may be required to get the approval of the supermarket manager. Once you have your survey results, work out the following: a) Are the data collected a population or a sam ple? How many observations did you collect? b) Graph the data and discuss the shape of the distribution. c) What is the mean? d) What is the standard deviation? e) Find a 90% and a 95% confidence interval for the average spending and what assumption you are making. f) Find a 90% and a 95% confidence interval for the variance and state what assumption you are making. g) What is the number of observations that you must collect if you want to be 95% confident that your error of estimation does not exceed $15? What assumption did you make?
24/08/11 7:42 PM