Statistics 1
Q1.
A camp director is interested in the mean number of letters each child sends during his or her camp session. The population standard deviation is known to be 2.5. A survey of 20 campers is taken. The mean from the sample is 7.9 with a sample standard deviation of 2.8.
(a).
(i). What is the sample statistic for the mean?
Soln.
(ii).What is the population parameter for the standard deviation?
Soln.
(iii). What is the sample size?
Soln.
(b). Define the random variables X and Xbar in words.
Soln.
(c). What distribution should be used for this problem? Explain your choice.
Soln.
(d). Construct a 90% confidence interval for the population mean number of letters campers sent home and interpret your results in the context of the question.
Soln.
(e). What will happen to the margin of error and confidence interval if 500 campers are surveyed? and why?
Soln.
Q2.
The Federal Election Commission collects information about campaign contributions and disbursements for candidates and political committees each election cycle. During the 2012 campaign season, there were 1,619 candidates for the House of Representatives across the United States who received contributions from individuals. Table shows the total receipts from individuals for a random selection of 40 House candidates rounded to the nearest $100. The standard deviation for this data to the nearest hundred is σ = $909,200.
$3,600 $1,243,900 $10,900 $385,200 $581,500
$7400 $2,900 $400 $3,714,500 $632,500
$391,000 $467,400 $56,800 $5,800 $405,200
$733,200 $8,000 $468,700 $75,200 $41,000
$13,300 $9,500 $953,800 $1,113,500 $1,109,300
$359,900 $986,100 $88,600 $378,200 $13,200
$3,800 $745,100 $5,800 $3,072,100 $1,626,700
$512,900 $2,309,200 $6,600 $202,400 $15,800
(a). Find the point estimate for the population mean.
Soln.
(b). Use the 95% confidence level to find the margin of error.
Soln.
(c). Calculate a 95% confidence interval for the mean total individual contributions.
Soln.
(d). Interpret the confidence interval in the context of the problem.
Soln.
Q3.
Forbes magazine published data on the best small firms in 2012. These were firms that had been publicly traded for at least a year, have a stock price of at least $5 per share, and have reported annual revenue between $5 million and $1 billion. The table below shows the ages of the corporate CEO’s for a random sample of these firms.
48 58 51 61 56
59 74 63 53 50
59 60 60 57 46
55 63 57 47 55
57 43 61 62 49
67 67 55 55 49
(a). Use Stat crunch or any software of your choice to calculate
(i). The sample mean of the ages of these CEO’s.
Soln.
(ii). The sample standard deviation of the ages of these CEO’s.
Soln.
(b).
(i). Use the t- distribution to construct a 90% confidence interval for the mean age of these CEO’s.
Soln.
(i). Use the t- distribution to construct a 95% confidence interval for the mean age of these CEO’s.
Soln.
(c). Which of the confidence intervals in b (i) and (ii) gives the more precise estimate? Explain your choice.
Soln.
