MATHEMATICS
4.
A family is relocating from St. Louis, Missouri, to California. Due to an increasing inventory of houses in St. Louis, it is taking longer than before to sell a house. The wife is concerned and wants to know when it is optimal to put their house on the market. They ask their realtor friend for help and she informs them that the last 26 houses that sold in their neighborhood took an average time of 218 days to sell. The realtor also tells them that based on her prior experience, the population standard deviation is 72 days. Use Table 1. 
a.  What assumption regarding the population is necessary for making an interval estimate for the population mean?  

b.  Construct a 90% confidence interval for the mean sale time for all homes in the neighborhood. (Round intermediate calculations to 4 decimal places, “z” value and final answers to 2 decimal places.) 
Confidence interval  PRIVATE “<INPUT TYPE=\”text\” SIZE=\”7\” NAME=\”Q_13252699393847620_ans2\” VALUE=\”\”>” MACROBUTTON HTMLDirect  to  PRIVATE “<INPUT TYPE=\”text\” SIZE=\”7\” NAME=\”Q_13252699393847620_ans3\” VALUE=\”\”>” MACROBUTTON HTMLDirect 
5.
We use the t distribution for the statistical inference of the population mean when the underlying population standard deviation is not known. Under the assumption that the population is normally distributed, find t_{α}_{/2,df} for the following scenarios. Use Table 2. (Round your answers to 3 decimal places.) 
t_{α}_{/2,df }  
a. A 90% confidence level and a sample of 28 observations.  PRIVATE “<INPUT TYPE=\”text\” SIZE=\”7\” NAME=\”Q_13252700138468585_ans1\” VALUE=\”\”>” MACROBUTTON HTMLDirect 
b. A 95% confidence level and a sample of 28 observations.  PRIVATE “<INPUT TYPE=\”text\” SIZE=\”7\” NAME=\”Q_13252700138468585_ans2\” VALUE=\”\”>” MACROBUTTON HTMLDirect 
c. A 90% confidence level and a sample of 15 observations.  PRIVATE “<INPUT TYPE=\”text\” SIZE=\”7\” NAME=\”Q_13252700138468585_ans3\” VALUE=\”\”>” MACROBUTTON HTMLDirect 
d. A 95% confidence level and a sample of 15 observations.  PRIVATE “<INPUT TYPE=\”text\” SIZE=\”7\” NAME=\”Q_13252700138468585_ans4\” VALUE=\”\”>” MACROBUTTON HTMLDirect 

6.
Let the following sample of 8 observations be drawn from a normal population with unknown mean and standard deviation: 22, 18, 14, 25, 17, 28, 15, 21. Use Table 2. 
a.  Calculate the sample mean and the sample standard deviation. (Round intermediate calculations to 4 decimal places, “sample mean” to 3 decimal places and “sample standard deviation” to 2 decimal places.) 
Sample mean  PRIVATE “<INPUT TYPE=\”text\” SIZE=\”7\” NAME=\”Q_13252699393847628_ans1\” VALUE=\”\”>” MACROBUTTON HTMLDirect 
Sample standard deviation  PRIVATE “<INPUT TYPE=\”text\” SIZE=\”7\” NAME=\”Q_13252699393847628_ans2\” VALUE=\”\”>” MACROBUTTON HTMLDirect 

b.  Construct the 80% confidence interval for the population mean. (Round “t” value to 3 decimal places, and final answers to 2 decimal places.) 
Confidence interval  PRIVATE “<INPUT TYPE=\”text\” SIZE=\”7\” NAME=\”Q_13252699393847628_ans3\” VALUE=\”\”>” MACROBUTTON HTMLDirect  to  PRIVATE “<INPUT TYPE=\”text\” SIZE=\”7\” NAME=\”Q_13252699393847628_ans4\” VALUE=\”\”>” MACROBUTTON HTMLDirect 
c.  Construct the 90% confidence interval for the population mean. (Round “t” value to 3 decimal places, and final answers to 2 decimal places.) 
Confidence interval  PRIVATE “<INPUT TYPE=\”text\” SIZE=\”7\” NAME=\”Q_13252699393847628_ans5\” VALUE=\”\”>” MACROBUTTON HTMLDirect  to  PRIVATE “<INPUT TYPE=\”text\” SIZE=\”7\” NAME=\”Q_13252699393847628_ans6\” VALUE=\”\”>” MACROBUTTON HTMLDirect 
d.  What happens to the margin of error as the confidence level increases from 80% to 90%?  

7.
The Chartered Financial Analyst (CFA^{®}) designation is fast becoming a requirement for serious investment professionals. Although it requires a successful completion of three levels of grueling exams, it also entails promising careers with lucrative salaries. A student of finance is curious about the average salary of a CFA^{®} charterholder. He takes a random sample of 36 recent charterholders and computes a mean salary of $158,000 with a standard deviation of $36,000. Assuming a normal distribution, use this sampleinformation to determine the 95% confidence interval for the average salary of a CFA charterholder.Use Table 2. (Round intermediate calculations to 4 decimal places, “t” value to 3 decimal places, and final answers to the nearest whole number.) 
Confidence interval  PRIVATE “<INPUT TYPE=\”text\” SIZE=\”7\” NAME=\”Q_13252700657501283_ans1\” VALUE=\”\”>” MACROBUTTON HTMLDirect  to  PRIVATE “<INPUT TYPE=\”text\” SIZE=\”7\” NAME=\”Q_13252700657501283_ans2\” VALUE=\”\”>” MACROBUTTON HTMLDirect 