# MATHEMATICS

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

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