a sports marketing company is interested in how many hours teenagers in a town spend watching sports. they…

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)

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)

Answer

Answer:

(4.865, 7.635)

Explanation:

Step1: Determine degrees of freedom

$n = 40$, $df=n - 1=39$

Step2: Find t - value for 90% confidence

From t - table, for $df = 39$ and 90% confidence, $t_{\alpha/2}\approx 1.685$

Step3: Calculate margin of error

$E=t_{\alpha/2}\frac{s}{\sqrt{n}}=1.685\times\frac{4.33}{\sqrt{40}}\approx1.385$

Step4: Calculate confidence interval

Lower limit: $\bar{x}-E = 6.25-1.385 = 4.865$ Upper limit: $\bar{x}+E=6.25 + 1.385=7.635$