you work for a chain of hamburger restaurants and want to estimate the population mean of the wait times in…

you work for a chain of hamburger restaurants and want to estimate the population mean of the wait times in the drive - thru for all customers. to do so, you select a random sample of 40 of the chains drive - thru customers and record the wait time in the drive - thru for each. assume it is known that the population standard deviation of the wait times in the drive - thru for the hamburger chains restaurants is 2.91 minutes. based on your sample, follow the steps below to construct a 90% confidence interval for the population mean of the wait times in the drive - thru for all customers. (if necessary, consult a list of formulas.) (a) click on \take sample\ to see the results from your random sample of 40 customers. enter the values of the sample size, the point estimate for the population mean, the population standard deviation, and the critical value you need for your 90% confidence interval. (choose the correct critical value from the table of critical values provided.) when you are done, select \compute\.

you work for a chain of hamburger restaurants and want to estimate the population mean of the wait times in the drive - thru for all customers. to do so, you select a random sample of 40 of the chains drive - thru customers and record the wait time in the drive - thru for each. assume it is known that the population standard deviation of the wait times in the drive - thru for the hamburger chains restaurants is 2.91 minutes. based on your sample, follow the steps below to construct a 90% confidence interval for the population mean of the wait times in the drive - thru for all customers. (if necessary, consult a list of formulas.) (a) click on \take sample\ to see the results from your random sample of 40 customers. enter the values of the sample size, the point estimate for the population mean, the population standard deviation, and the critical value you need for your 90% confidence interval. (choose the correct critical value from the table of critical values provided.) when you are done, select \compute\.

Answer

Explanation:

Step1: Identify sample - size

The sample size $n = 40$.

Step2: Determine point - estimate

The point - estimate for the population mean is the sample mean. But since the sample results are not given, we assume it is $\bar{x}$ (unknown for now). Here we focus on the general process.

Step3: Identify population standard deviation

The population standard deviation $\sigma=2.91$.

Step4: Find critical value

For a 90% confidence interval, the critical value $z_{\alpha/2}=z_{0.05}=1.645$.

Step5: Calculate standard error

The formula for the standard error $SE=\frac{\sigma}{\sqrt{n}}$. Substituting $\sigma = 2.91$ and $n = 40$, we get $SE=\frac{2.91}{\sqrt{40}}\approx\frac{2.91}{6.3246}\approx0.46$.

Step6: Calculate margin of error

The margin of error $E = z_{\alpha/2}\times SE$. Substituting $z_{\alpha/2}=1.645$ and $SE\approx0.46$, we get $E=1.645\times0.46\approx0.76$.

Step7: Construct confidence interval

The 90% confidence interval for the population mean $\mu$ is $\bar{x}-E<\mu<\bar{x} + E$.

If we assume we have a sample mean $\bar{x}$ (not given in the problem), the confidence interval would be calculated as above.

Answer:

Sample size: 40 Point estimate: (unknown, represented as $\bar{x}$) Population standard deviation: 2.91 Critical value: 1.645 Standard error: $\frac{2.91}{\sqrt{40}}\approx0.46$ Margin of error: $1.645\times0.46\approx0.76$ 90% confidence interval: $\bar{x}- 0.76<\mu<\bar{x}+0.76$