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How will you interpret a \(99 \%\) confidence interval for \(\mu ?\) Explain.

The standard deviation for a population is \(\sigma=14.8\). A random sample of 25 observations selected from this population gave a mean equal to \(143.72\). The population is known to have a normal distribution. a. Make a \(99 \%\) confidence interval for \(\mu\). b. Construct a \(95 \%\) confidence interval for \(\mu\). c. Determine a \(90 \%\) confidence interval for \(\mu\). d. Does the width of the confidence intervals constructed in parts a through \(\mathrm{c}\) decrease as the confidence level decreases? Explain your answer.

The standard deviation for a population is \(\sigma=7.14\). A random sample selected from this population gave a mean equal to \(48.52\). a. Make a \(95 \%\) confidence interval for \(\mu\) assuming \(n=196\). b. Construct a \(95 \%\) confidence interval for \(\mu\) assuming \(n=100\). c. Determine a \(95 \%\) confidence interval for \(\mu\) assuming \(n=49\). d. Does the width of the confidence intervals constructed in parts a through c increase as the sample size decreases? Explain.

For a population, the value of the standard deviation is \(2.65\). A random sample of 35 observations taken from this population produced the following data. \(\begin{array}{lllllll}42 & 51 & 42 & 31 & 28 & 36 & 49 \\ 29 & 46 & 37 & 32 & 27 & 33 & 41 \\ 47 & 41 & 28 & 46 & 34 & 39 & 48 \\ 26 & 35 & 37 & 38 & 46 & 48 & 39 \\ 29 & 31 & 44 & 41 & 37 & 38 & 46\end{array}\) a. What is the point estimate of \(\mu\) ? b. Make a \(98 \%\) confidence interval for \(\mu\). c. What is the margin of error of estimate for part b?

A bank manager wants to know the mean amount of mortgage paid per month by homeowners in an area. A random sample of 120 homeowners selected from this area showed that they pay an average of \(\$ 1575\) per month for their mortgages. The population standard deviation of all such mortgages is \(\$ 215\). a. Find a \(97 \%\) confidence interval for the mean amount of mortgage paid per month by all homeowners in this area. b. Suppose the confidence interval obtained in part a is too wide. How can the width of this interval be reduced? Discuss all possible alternatives. Which alternative is the best?

A city planner wants to estimate the average monthly residential water usage in the city at a \(97 \%\) confidence level. Based on earlier data, the population standard deviation of the monthly residential water usage in this city is \(389.60\) gallons. How large a sample should be selected so that the estimate for the average monthly residential water usage in this city is within 100 gallons of the population mean?

A random sample of 11 observations taken from a normally distributed population produced the following data: $$ \begin{array}{lllllllllll} -7.1 & 10.3 & 8.7 & -3.6 & -6.0 & -7.5 & 5.2 & 3.7 & 9.8 & -4.4 & 6.4 \end{array} $$ a. What is the point estimate of \(\mu\) ? b. Make a \(95 \%\) confidence interval for \(\mu\). c. What is the margin of error of estimate for \(\mu\) in part b?

Suppose, for a random sample selected from a normally distributed population, \(\bar{x}=68.50\) and \(s=8.9\). a. Construct a \(95 \%\) confidence interval for \(\mu\) assuming \(n=16\). b. Construct a \(90 \%\) confidence interval for \(\mu\) assuming \(n=16\). Is the width of the \(90 \%\) confidence interval smaller than the width of the \(95 \%\) confidence interval calculated in part a? If yes, explain why. c. Find a \(95 \%\) confidence interval for \(\mu\) assuming \(n=25\). Is the width of the \(95 \%\) confidence interval for \(\mu\) with \(n=25\) smaller than the width of the \(95 \%\) confidence interval for \(\mu\) with \(n=16\) calculated in part a? If so, why? Explain.

a. A random sample of 400 observations taken from a population produced a sample mean equal to \(92.45\) and a standard deviation equal to \(12.20\). Make a \(98 \%\) confidence interval for \(\mu\). b. Another sample of 400 observations taken from the same population produced a sample mean equal to \(91.75\) and a standard deviation equal to \(14.50 .\) Make a \(98 \%\) confidence interval for \(\mu\). c. A third sample of 400 observations taken from the same population produced a sample mean equal to \(89.63\) and a standard deviation equal to \(13.40 .\) Make a \(98 \%\) confidence interval for \(\mu\). d. The true population mean for this population is \(90.65\). Which of the confidence intervals constructed in parts a through \(\mathrm{c}\) cover this population mean and which do not?

activities (playing games, personal communications, etc.) during this month are as follows: $$ \begin{array}{lllllllll} 7 & 12 & 9 & 8 & 11 & 4 & 14 & 1 & 6 \end{array} $$ Assuming that such times for all employees are approximately normally distributed, make a \(95 \%\) confidence interval for the corresponding population mean for all employees of this company.A company randomly selected nine office employees and secretly monitored their computers for one month. The times (in hours) spent by these employees using their computers for non- job-related