Construct a $95\%$confidence interval for the population mean time spent waiting. State the confidence interval, sketch the graph, and calculate the error bound .

Given in the question that , A hospital is trying to cut down on emergency room wait times. It is interested in the amount of time patients must wait before being called back to be examined. An investigation committee randomly surveyed $70$patients. The sample mean was $1.5$hours with a sample standard deviation of $0.5$hours.

The sample mean is $\overline{x}=1.5$

The random sample is, $n=70$

The sample standard deviation is$s=0.5$

Now calculate the confidence interval using $TI-83$calculator using the steps given below,

Press STAT and use the arrow (?) to TESTS.

Then press the arrow$(\downarrow )$to 8 : TInterval and press enter.

Next, use the arrow $(\to )$to STARTS and press enter.

Then, press the arrow$(?)$and enter the inputs as shown below,

Step 5: Then press the arrow$(?)$to calculator and press enter. The output is given below,

The $95\%$confidence interval for the population mean time spent waiting is $[1.38,1.62]$

The graph is given below,

The error bound is calculated using the formula given below,

$EBM=\frac{(\text{Upper bound}-\text{lower bound})}{2}$

The calculation is given below,

$EBM=\frac{(1.62-1.38)}{2}$

localid="1648455872595" $=\frac{0.24}{2}$

$=0.12$