Problem 1:
A random sample of n = 9 values taken from a normally distributed population resulted in the following sample values:
107 109 99 91 103 105
105 94 107 94 97 113
Use the sample information to construct 95% confidence interval estimate for the population mean.
This is the only problem this week that MUST be done using "hand" calculations. You can use words to describe the equations (for example, "x-bar + or - 1.96 x square root of the standard deviation"), and/or you can use the Microsoft Equation Editor (Equation 3) in Word, which is not intuitive. Text is fine with me.
Problem 2:
The BelSante Company operates retail pharmacies in 10 Eastern states. Recently, the company's internal audit department selected a random sample of 300 prescriptions issues throughout the system. The objective of the sampling was to estimate the average dollar value of all prescriptions issues by the company. The following data were collected:
x¯ = $14.23
s = 3.00
- Determine the 90% confidence interval estimate for the true average sales value for prescriptions issues by the company. Interpret the interval estimate.
- One of its retail outlets recently reported that it had monthly revenue of $7,392 from 528 prescriptions. Are such results to be expected? Do you believe that the retail outlet should be audited? Support your answer with calculations and logic.
you can use PhStat: Confidence intervals > Estimate for the mean, sigma unknown. Part b is "on your own".
Problem-3:
Determine the smallest sample size required to estimate the population man under the following specifications:
- e = 2.4, confidence level = 80%, data between 50 and 150
d. e = 1.2, confidence level = 90%, data between 25 and 175
a and d only. In this problem, you are given e and z, which are two of the three pieces of information you need to use. You will need to estimate the standard deviation. To do this, think about the empirical rule, and ask yourself how many standard deviations, in a normal curve, lie from one end of the curve to the other.
Problem 4:
The Longmont Computer Leasing Company leases computers and peripherals like laser printers. The printers have a counter that keeps track of the number of pages printed. The company wishes to estimate the mean number of pages that will be printed in a month on its leased printers. The plan is to select a random sample of printers and record the number on each printer's counter at the beginning of May. Then, at the end of May, the number on the counter will be recorded again and the difference will be the number of copies on that printer for the month. The company wants the estimate to be within +/-100 pages of the true mean with a 95% confidence level.
- The standard deviation in pages printed is thought to be about 1,400 pages. How many printers should be sampled?
- Suppose the conjecture concerning the size of the standard deviation is off (plus or minus) by as much as 10%. What percentage change in the required sample size would this produce?
Use PhStat > Sample Size > Determination for the mean. For part b, you have two calculations: (1) you'll need to first increase the standard deviation by 10%, calculate the sample size resulting from this, and calculate the percentage change in sample size; (2) then, do another calculation, this time decreasing the standard deviation by 10%, recalculate the sample size required, and calculate the percentage reduction in sample size. In other words, you will have one sample size answer for 8-40a, and two sample size answers (and the percentage change in the sample size) for 8-40b.
Problem 8-58:
The television landscape has certainly been changing in recent years as satellite and cable television providers compete for old-line television networks' viewers. In fact, prior to 2005, the networks had lost viewers in the 18-49 age group for over 10 consecutive years, according to a May 2005 article in the Wall Street Journal by Brooks Barnes. However, according to the article, in 2005 the networks would post their first gain in viewers. Suppose that CBS plans to conduct interviews with television viewers in an attempt to estimate the proportion of viewers in the 18-49 age group who watch "most" of their television on network television as opposed to cable or satellite. CBS wishes to have 95% confidence and a margin of error in its estimate of +/-0.03. A pilot sample of size 50 was selected, and the sample proportion was 0.61. To achieve these results with a simple random sample, how many additional viewers should be sampled?
Use PhStat > Sample Size > Determination for the proportion.
Problem 8-71:
Explain why the critical value for a given confidence level when the population variance is not known is always greater than the critical value for the same confidence level when the population variance is known.
Problem 8-76:
According to an investigative reporter (Jim Drinkard, "Legislators Want to Ground 'Fact Finding' Trips," USA Today, January 19, 2006), members of Congress are coming under scrutiny for "Fact-Finding" trips. Since 2000, members of Congress have made 6,666 trips paid for by private interests. The trips were worth about $19.6 million.
- Calculate the average cost of these fact-finding trips.
- If the cost of the trips could be considered to have a normal distribution, determine the standard deviation of the cost of the trips. (Hint: Recall the Empirical Rule.)
- Choose a reasonable confidence level and calculate a confidence interval for the average cost of congressional fact-finding trips from the year 2000 until January 19, 2006.
[i]
1. Click where you want to insert the equation.
2. On the Insert menu, click Object, and then click the Create New tab.
3. In the Object type box, click Microsoft Equation 3.0.
If Microsoft Equation Editor is not available, you may need to install it.
How?
If you originally installed Microsoft Office from a network file server or from a shared folder, you must install Equation Editor from that location. If you installed Office from a CD-ROM, you must install Equation Editor from the disc.
1. Quit all programs.
2. Do one of the following:
§ If you run Microsoft Windows 2000, double-click the Add/Remove Programs icon in Control Panel.
§ If you run Microsoft Windows XP, click Add or Remove Programs in Control Panel.
3. In the Currently installed programs box, click the listing for Microsoft Office or Microsoft Word, depending on whether you installed Word as part of Office or as an individual program, and then click Change.
4. On the Maintenance Mode Options screen, click Add or Remove Features, and then click Next.
5. If a Custom Setup screen appears, select the Choose advanced customization of applications check box, and then click Next.
6. In the list of features to install, click the expand indicator (+) next to Office Tools.
7. Click the arrow next to Equation Editor, and then click Run from My Computer.
8. Click Update.
9. Restart Word.
4. Click OK.
5. Build the equation by selecting symbols from the Equation toolbar (toolbar: A bar with buttons and options that you use to carry out commands. To display a toolbar, press ALT and then SHIFT+F10.) and by typing variables and numbers. From the top row of the Equation toolbar, you can choose from more than 150 mathematical symbols. From the bottom row, you can choose from a variety of templates or frameworks that contain symbols such as fractions, integrals, and summations.
If you need help, click Equation Editor Help Topics on the Help menu.
6. To return to Microsoft Word, click the Word document.