Question

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.

Identify the following:

a. $\overline{x}$=_______

b. $s_x$=_______

c. n =_______

d. n – 1 =_______

Short answer

(a) $\overline{x}=151$hours

(b) $s_x=32$hours

(c) $n=151$

(d)$n-1=107$

Step-by-step solution

Part (a) Step 1: Given information

No. of patients surveyed $=108$

Sample Mean $=151$hours

Sample Standard Deviation $=32$hours

Part (b) Step 2: Explanation

From the given values

The sample mean $\overline{x}$is computed by adding all of the sample's observations and then dividing it by the number of observations in the sample.

It is stated explicitly in the question that the sample mean is$151$ hours.

Part (b) Step 1: Given information

No. of patients surveyed $=108$

Sample Mean $=151$hours

Sample Standard Deviation $=32$hours

Part (b) Step 2: Explanation

$s_x$Defines the sample standard deviation, which shows us how far your data has drifted or strayed from the mean.

The sample standard deviation describes how far your sample deviates from the mean. It is stated explicitly in this question that the sample standard deviation is$32$ hours.

Part (c) Step 1: Given information

No. of patients surveyed $=108$

Sample Mean $=151$hours

Sample Standard Deviation $=32$hours

Part (c) Step 2: Explanation

The sample size is denoted by $n$, which means the total number of observations in the sample is denoted by $n$.

It is stated explicitly in this question that the sample size is$151$.

Part (d) Step 1: Given information

No. of patients surveyed $=108$

Sample Mean $=151$hours

Sample Standard Deviation $=32$hours

Part (d) Step 2: Explanation

The degree of freedom is defined by $n$.

In this question, it is stated that $108$Americans were polled, which means that $n$equals $108$and

$n-1=108-1$

$=107$.