MATHEMATICS
8.
The monthly closing stock prices (rounded to the nearest dollar) for Panera Bread Co. for the first six months of 2010 are reported in the following table. Use Table 2. 
Months  Closing Stock Price 
January 2010  $71 
February 2010  73 
March 2010  76 
April 2010  78 
May 2010  81 
June 2010  75 

SOURCE: http://finance.yahoo.com.
a.  Calculate the sample mean and the sample standard deviation. (Round intermediate calculations to 4 decimal places and “sample mean” and “sample standard deviation” to 2 decimal places.) 
Sample mean  PRIVATE “<INPUT TYPE=\”text\” SIZE=\”7\” NAME=\”Q_13252699393847632_ans1\” VALUE=\”\”>” MACROBUTTON HTMLDirect 
Sample standard deviation  PRIVATE “<INPUT TYPE=\”text\” SIZE=\”7\” NAME=\”Q_13252699393847632_ans2\” VALUE=\”\”>” MACROBUTTON HTMLDirect 

b.  Compute the 90% confidence interval for the mean stock price of Panera Bread Co., assuming that the stock price is normally distributed. (Round “t” value to 3 decimal places, and final answers to 2 decimal places.) 
Confidence interval  PRIVATE “<INPUT TYPE=\”text\” SIZE=\”7\” NAME=\”Q_13252699393847632_ans3\” VALUE=\”\”>” MACROBUTTON HTMLDirect  to  PRIVATE “<INPUT TYPE=\”text\” SIZE=\”7\” NAME=\”Q_13252699393847632_ans4\” VALUE=\”\”>” MACROBUTTON HTMLDirect 
c.  What happens to the margin of error if a higher confidence level is used for the interval estimate?  

9.
A random sample of 80 observations results in 50 successes. Use Table 1. 
a.  Construct a 95% confidence interval for the population proportion of successes. (Round intermediate calculations to 4 decimal places, “z” value to 2 decimal places, and final answers to 3 decimal places.) 
Confidence interval  PRIVATE “<INPUT TYPE=\”text\” SIZE=\”7\” NAME=\”Q_13252699393895835_ans1\” VALUE=\”\”>” MACROBUTTON HTMLDirect to PRIVATE “<INPUT TYPE=\”text\” SIZE=\”7\” NAME=\”Q_13252699393895835_ans2\” VALUE=\”\”>” MACROBUTTON HTMLDirect 
b.  Construct a 95% confidence interval for the population proportion of failures. (Round intermediate calculations to 4 decimal places, “z” value to 2 decimal places, and final answers to 3 decimal places.) 
Confidence interval  PRIVATE “<INPUT TYPE=\”text\” SIZE=\”7\” NAME=\”Q_13252699393895835_ans3\” VALUE=\”\”>” MACROBUTTON HTMLDirect to 
10.
In a recent poll of 760 homeowners in the United States, one in five homeowners reports having a home equity loan that he or she is currently paying off. Using a confidence coefficient of 0.90, derive an interval estimate for the proportion of all homeowners in the United States that hold a home equity loan. Use Table 1. (Round intermediate calculations to 4 decimal places, “z” value to 2 decimal places, and final answers to 3 decimal places.) 
Confidence interval  PRIVATE “<INPUT TYPE=\”text\” SIZE=\”7\” NAME=\”Q_13252699393847641_ans1\” VALUE=\”\”>” MACROBUTTON HTMLDirect to PRIVATE “<INPUT TYPE=\”text\” SIZE=\”7\” NAME=\”Q_13252699393847641_ans2\” VALUE=\”\”>” MACROBUTTON HTMLDirect 
11.
An accounting professor is notorious for being stingy in giving out good letter grades. In a large section of 140 students in the fall semester, she gave out only 5% As, 23% Bs, 42% Cs, and 30% Ds and Fs. Assuming that this was a representative class, compute a 95% confidence interval of the probability of getting at least a B from this professor. Use Table 1. (Round intermediate calculations to 4 decimal places, “z” value to 2 decimal places, and final answers to 3 decimal places.) 
Confidence interval  PRIVATE “<INPUT TYPE=\”text\” SIZE=\”7\” NAME=\”Q_13252700183777051_ans1\” VALUE=\”\”>” MACROBUTTON HTMLDirect to PRIVATE “<INPUT TYPE=\”text\” SIZE=\”7\” NAME=\”Q_13252700183777051_ans2\” VALUE=\”\”>” MACROBUTTON HTMLDirect 
12.
You need to compute a 99% confidence interval for the population mean. How large a sample should you draw to ensure that the sample mean does not deviate from the population mean by more than 1.2? (Use 6.0 as an estimate of the population standard deviation from prior studies.) Use Table 1. (Round intermediate calculations to 4 decimal places and “z” value to 2 decimal places. Round up your answer to the nearest whole number.) 
Sample size  PRIVATE “<INPUT TYPE=\”text\” SIZE=\”7\” NAME=\”Q_13252699393847645_ans1\” VALUE=\”\”>” MACROBUTTON HTMLDirect 
13.
In the planning stage, a sample proportion is estimated as = 40/50 = 0.80. Use this information to compute the minimum sample size n required to estimate p with 99% confidence if the desired margin of error E = 0.12. What happens to n if you decide to estimate p with 90% confidence? Use Table 1. (Round intermediate calculations to 4 decimal places and “z” value to 2 decimal places. Round up your answers to the nearest whole number.) 
Confidence Level  n 
99%  PRIVATE “<INPUT TYPE=\”text\” SIZE=\”7\” NAME=\”Q_13252699393895838_ans1\” VALUE=\”\”>” MACROBUTTON HTMLDirect 
90%  PRIVATE “<INPUT TYPE=\”text\” SIZE=\”7\” NAME=\”Q_13252699393895838_ans2\” VALUE=\”\”>” MACROBUTTON HTMLDirect 

14.
An analyst from an energy research institute in California wishes to precisely estimate a 99% confidence interval for the average price of unleaded gasoline in the state. In particular, she does not want the sample mean to deviate from the population mean by more than $0.06. What is the minimum number of gas stations that she should include in her sample if she uses the standard deviation estimate of $0.32, as reported in the popular press? Use Table 1. (Round intermediate calculations to 4 decimal places and “z” value to 2 decimal places. Round up your answer to the nearest whole number.) 
Minimum number of gas stations  PRIVATE “<INPUT TYPE=\”text\” SIZE=\”7\” NAME=\”Q_13252699393895840_ans1\” VALUE=\”\”>” MACROBUTTON HTMLDirect 
15.
A student of business is interested in estimating a 99% confidence interval for the proportion of students who bring laptops to campus. He wishes a precise estimate and is willing to draw a large sample that will keep the sample proportion within five percentage points of the population proportion. What is the minimum sample size required by this student, given that no prior estimate of the population proportion is available?Use Table 1. (Round intermediate calculations to 4 decimal places and “z” value to 2 decimal places. Round up your answer to the nearest whole number.) 
Minimum sample size  PRIVATE “<INPUT TYPE=\”text\” SIZE=\”7\” NAME=\”Q_13252700183670340_ans1\” VALUE=\”\”>” MACROBUTTON HTMLDirect 