# 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   %

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