Sales personnel for Skillings Distributors submit weekly reports listing the customer contacts made during the week. A sample of $65$ weekly reports showed a sample mean of $19.5$ customer contacts per week. The sample standard deviation was $5.2.$ Provide $90\%$ and $95\%$ confidence intervals for the population mean number of weekly customer contacts for the sales personnel.

The following sample data are from a normal population: $10,~ 8,~12,~ 15,~ 13,~ 11,~ 6,~ 5.$

With $95\%$ confidence, what is the margin of error for the estimation of the population mean?

A sample containing years to maturity and yield (%) for 40 corporate bonds is contained in the data file named CorporateBonds (Barron's, April 2, 2012).

a. Develop a scatter diagram of the data using x=years to maturity as the independent variable. Does a simple linear regression model appear to be appropriate?

b. Develop an estimated regression equation with x=years to maturity and $x^2$ as the independent variables.

c. As an alternative to fitting a second-order model, fit a model using the natural logarithm of price as the independent variable; that is, $\hat{y}=b_0+b_1 \ln (x)$. Does the estimated regression using the natural logarithm of x provide a better fit than the estimated regression developed in part (b)? Explain.

The International Air Transport Association surveys business travelers to develop quality ratings for transatlantic gateway airports. The maximum possible rating is 10 . Suppose a simple random sample of 50 business travelers is selected and each traveler is asked to provide a rating for the Miami International Airport. The ratings obtained from the sample of 50 business travelers follow.

$$\begin{array}{rrrrrrrrrrrrr}6 & 4 & 6 & 8 & 7 & 7 & 6 & 3 & 3 & 8 & 10 & 4 & 8 \\ 7 & 8 & 7 & 5 & 9 & 5 & 8 & 4 & 3 & 8 & 5 & 5 & 4 \\ 4 & 4 & 8 & 4 & 5 & 6 & 2 & 5 & 9 & 9 & 8 & 4 & 8 \\ 9 & 9 & 5 & 9 & 7 & 8 & 3 & 10 & 8 & 9 & 6 & & \end{array}$$

Develop a 95% confidence interval estimate of the population mean rating for Miami.

Find the $t$ value(s) for each of the following cases.

Upper tail area of $0.025$ with $12$ degrees of freedom.

A simple random sample with $n=54$ provided a sample mean of $22.5$ and a sample standard deviation of $4.4.$

Develop a $90\%$ confidence interval for the population mean.

A simple random sample of 40 items resulted in a sample mean of $25.$ The population standard deviation is $\sigma =5.$

What is the standard error of the mean, $\sigma_{\bar{x}}$?

In developing patient appointment schedules, a medical center wants to estimate the mean time that a staff member spends with each patient. How large a sample should be taken if the desired margin of error is two minutes at a $95\%$ level of confidence? How large a sample should be taken for a $99\%$ level of confidence? Use a planning value for the population standard deviation of eight minutes.

A simple random sample of $50$ items from a population with $\sigma= 6$ resulted in a sample mean of $32.$

Provide a $90\%$ confidence interval for the population mean.

Sales personnel for Skillings Distributors submit weekly reports listing the customer contacts made during the week. A sample of 65 weekly reports showed a sample mean of $19.5$ customer contacts per week. The sample standard deviation was 5.2. Provide $90 \%$ and $95 \%$ confidence intervals for the population mean number of weekly customer contacts for the sales personnel.

Employment in Older Workers. Older people often have a hard time finding work. AARP reported on the number of weeks it takes a worker aged 55 plus to find a job. The data on number of weeks spent searching for a job contained in the file JobSearch are consistent with the AARP findings.

a. Provide a point estimate of the population mean number of weeks it takes a worker aged 55 plus to find a job.

How large a sample should be selected to provide a $95$ confidence interval with a margin of error of $10$? Assume that the population standard deviation is $40.$

Employment in Older Workers. Older people often have a hard time finding work. AARP reported on the number of weeks it takes a worker aged 55 plus to find a job. The data on number of weeks spent searching for a job contained in the file JobSearch are consistent with the AARP findings.

b. At $95 \%$ confidence, what is the margin of error?

The following sample data are from a normal population: $10,~ 8,~12,~ 15,~ 13,~ 11,~ 6,~ 5.$

What is the point estimate of the population standard deviation?