Question

Construct a $99\%$confidence interval for the population mean hours spent watching television per month.

(a) State the confidence interval

(b) sketch the graph, and

(c) calculate the error bound.

Short answer

(a) The $99\%$confidence interval for the population mean hours spent watching television per month is$[142.92,159.08]$

(b)

(c)The error bound for mean is $8.08$

Step-by-step solution

Part (a) Step 1: Given information

Given in the question that, One hundred eight Americans were surveyed to determine the number of hours they spend watching television each month. It was revealed that they watched an average of $151$hours each month with a standard deviation of $32$hours. Assume that the underlying population distribution is normal.

Part (a) Step 2: Explanation

The sample mean $\overline{x}=151$

A random sample is, $n=108$

The sample standard deviation is$s=32$

Now estimate the confidence interval using the 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.

Then use the arrow $(\to )$to STATS and press enter.

Now 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

Part (b) Step 1:Given information

One hundred eight Americans were surveyed to determine the number of hours they spend watching television each month. It was revealed that they watched an average of $151$hours each month with a standard deviation of $32$hours. Assume that the underlying population distribution is normal.

Part (b) Step 2: Graphical representation

The graph is given below,

Part (c) Step 1: Given information

Given in the question that, One hundred eight Americans were surveyed to determine the number of hours they spend watching television each month. It was revealed that they watched an average of $151$hours each month with a standard deviation of$32$ hours. Assume that the underlying population distribution is normal.

Part (c) Step 2: Explanation

The error bound is calculated using the formula given below,

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

The calculation is given below,

$EBM=\frac{(159.08-142.92)}{2}$

$=\frac{16.16}{2}$

$=8.08$.