Questions: Questions 13 and 14, use the following information: a Internet provider contacts a random sample of 300 customers and asks how many hours per week the customers use the Internet. The average amount of time spent on the Internet per week was 7.2 hours, with a standard deviation of 7.9 hours. 13) Construct a 95% confidence interval for the average amount of time customers of this Internet provider spend on the Internet each week. Round the margin of error to one decimal place. Also, Provide an interpretation of your interval in the context of this data situation. A) 6.3 to 8.1 hours C) 5.7 to 8.7 hours B) 6.0 to 8.4 hours D) 5.5 to 8.9 hours

Questions 13 and 14, use the following information:
a Internet provider contacts a random sample of 300 customers and asks how many hours per week the customers use the Internet. The average amount of time spent on the Internet per week was 7.2 hours, with a standard deviation of 7.9 hours.
13) Construct a 95% confidence interval for the average amount of time customers of this Internet provider spend on the Internet each week. Round the margin of error to one decimal place.
Also, Provide an interpretation of your interval in the context of this data situation.
A) 6.3 to 8.1 hours
C) 5.7 to 8.7 hours
B) 6.0 to 8.4 hours
D) 5.5 to 8.9 hours

Transcript text: Questions 13 and 14, use the following information: a Internet provider contacts a random sample of 300 customers and asks how many hours per week the customers use the Internet. The average amount of time spent on the Internet per week was 7.2 hours, with a standard deviation of 7.9 hours. 13) Construct a $95 \%$ confidence interval for the average amount of time customers of this Internet provider spend on the Internet each week. Round the margin of error to one decimal place. Also, Provide an interpretation of your interval in the context of this data situation. A) 6.3 to 8.1 hours C) 5.7 to 8.7 hours B) 6.0 to 8.4 hours D) 5.5 to 8.9 hours

Solution

Solution Steps

Step 1: Calculate the Margin of Error

To calculate the margin of error ($E$), we use the formula:

\[ E = Z \cdot \frac{\sigma}{\sqrt{n}} \]

where:

$Z = 2.0$ (Z-Score for 95% confidence level),
$\sigma = 7.9$ (standard deviation),
$n = 300$ (sample size).

Substituting the values, we have:

\[ E = 2.0 \cdot \frac{7.9}{\sqrt{300}} \approx 0.9 \]

Step 2: Construct the Confidence Interval

The confidence interval for the mean is given by:

\[ \bar{x} \pm E \]

where:

$\bar{x} = 7.2$ (sample mean),
$E = 0.9$ (margin of error).

Thus, the confidence interval is:

\[ (7.2 - 0.9, 7.2 + 0.9) = (6.3, 8.1) \]

Step 3: Interpretation of the Confidence Interval

We interpret the confidence interval as follows:

We are 95% confident that the true average amount of time customers of this Internet provider spend on the Internet each week is between $6.3$ and $8.1$ hours.