# Mathematics

Homework  chapter 8 (1-15)

–          Table 1 : z table

–          Table 2: df  table

1.

 A simple random sample of 25 observations is derived from a normally distributed population with a known standard deviation of 8.2. Use Table 1.

a. Is the condition that   is normally distributed satisfied?

 PRIVATE “” MACROBUTTON HTMLDirect Yes PRIVATE “” MACROBUTTON HTMLDirect No

 b. Compute the margin of error with 80% confidence. (Round intermediate calculations to 4 decimal places, “z” value and final answer to 2 decimal places.)

 Margin of error PRIVATE “” MACROBUTTON HTMLDirect

 c. Compute the margin of error with 90% confidence. (Round intermediate calculations to 4 decimal places, “z” value and final answer to 2 decimal places.)

 Margin of error PRIVATE “” MACROBUTTON HTMLDirect

d. Which of the two margins of error will lead to a wider interval?

 PRIVATE “” MACROBUTTON HTMLDirect The margin of error with 90% confidence. PRIVATE “” MACROBUTTON HTMLDirect The margin of error with 80% confidence.

2.

 Consider a population with a known standard deviation of 26.8. In order to compute an interval estimate for the population mean, a sample of 64 observations is drawn. Use Table 1.

a. Is the condition that   is normally distributed satisfied?

 PRIVATE “” MACROBUTTON HTMLDirect Yes PRIVATE “” MACROBUTTON HTMLDirect No

 b. Compute the margin of error at a 95% confidence level. (Round your intermediate calculations to 4 decimal places. Round “z” value and final answer to 2 decimal places.)

 Margin of error PRIVATE “” MACROBUTTON HTMLDirect

 c. Compute the margin of error at a 95% confidence level based on a larger sample of 225 observations.(Round your intermediate calculations to 4 decimal places. Round “z” value and final answer to 2 decimal places.)

 Margin of error PRIVATE “” MACROBUTTON HTMLDirect

d. Which of the two margins of error will lead to a wider confidence interval?

 PRIVATE “” MACROBUTTON HTMLDirect 95% confidence with n = 64. PRIVATE “” MACROBUTTON HTMLDirect 95% confidence with n = 225.

3.

 In order to estimate the mean 30-year fixed mortgage rate for a home loan in the United States, a random sample of 28 recent loans is taken. The average calculated from this sample is 5.25%. It can be assumed that 30-year fixed mortgage rates are normally distributed with a standard deviation of 0.50%. Compute 90% and 99% confidence intervals for the population mean 30-year fixed mortgage rate. Use Table 1.(Round intermediate calculations to 4 decimal places, “z” value and final answers to 2 decimal places. Enter your answers as percentages, not decimals.)

 Confidence Level Confidence Interval 90% PRIVATE “” MACROBUTTON HTMLDirect   % to PRIVATE “” MACROBUTTON HTMLDirect   % 99% PRIVATE “” MACROBUTTON HTMLDirect   % to PRIVATE “” MACROBUTTON HTMLDirect   %

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?

 PRIVATE “” MACROBUTTON HTMLDirect Assume that the central limit theorem applies. PRIVATE “” MACROBUTTON HTMLDirect Assume that the population has a normal distribution.

 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 “” MACROBUTTON HTMLDirect to PRIVATE “” 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 tα/2,df for the following scenarios. Use Table 2. (Round your answers to 3 decimal places.)

 tα/2,df a. A 90% confidence level and a sample of 28 observations. PRIVATE “” MACROBUTTON HTMLDirect b. A 95% confidence level and a sample of 28 observations. PRIVATE “” MACROBUTTON HTMLDirect c. A 90% confidence level and a sample of 15 observations. PRIVATE “” MACROBUTTON HTMLDirect d. A 95% confidence level and a sample of 15 observations. PRIVATE “” 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 “” MACROBUTTON HTMLDirect Sample standard deviation PRIVATE “” 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 “” MACROBUTTON HTMLDirect to PRIVATE “” 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 “” MACROBUTTON HTMLDirect to PRIVATE “” MACROBUTTON HTMLDirect

d. What happens to the margin of error as the confidence level increases from 80% to 90%?

 PRIVATE “” MACROBUTTON HTMLDirect As the confidence level increases, the interval becomes wider. PRIVATE “” MACROBUTTON HTMLDirect As the confidence level increases, the interval becomes narrower.

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 “” MACROBUTTON HTMLDirect to PRIVATE “” MACROBUTTON HTMLDirect

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