A sports marketing company is interested in how many hours teenagers in a town spend watching sports. They randomly select 40 teenagers in this town and ask how many hours per week they spend watching sports. The mean amount is 6.25 hours with a standard deviation of 4.33 hours. Which of the following is the 90% confidence interval for the true mean amount of time teenagers from this town watch sports?

Find the t-table here.

(4.396, 8.104)
(4.865, 7.635)
(5.097, 7.404)
(5.245, 7.256)

Answers

Answer 1

Answer:

C. (5.097, 7.404)

Step-by-step explanation:

EDGE 2020

Answer 2

The 90% confidence interval for the true mean amount of time teenagers from this town watch sports is (5.097, 7.404).

What is Statistics?

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

The formula for the confidence interval is:

CI = x ± tα/2 × (s/√n)

where x is the sample mean,

s is the sample standard deviation,

n is the sample size, and

tα/2 is the t-value with (n-1) degrees of freedom and a confidence level of 90%.

From data (x) is 6.25 hours and

s=  4.33 hours.

We also know the sample size (n) is 40.

To find the t-value with (n-1) degrees of freedom and a confidence level of 90%, we can use a t-table.

For 39 degrees of freedom and a confidence level of 90%

Let us find that the t-value is 1.684.

Substituting the values we have into the formula, we get:

CI = 6.25 ± 1.684 × (4.33/√40)

CI = (5.097, 7.404)

Therefore, the 90% confidence interval for the true mean amount of time teenagers from this town watch sports is (5.097, 7.404).

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