To determine how many hours per week freshmen college students watch television, a random sample of 225 students was selected. It was determined that the students in the sample spent an average of 35 hours watching TV per week. The population standard deviation is known to be 12 hours. Provide a 95% confidence interval estimate for the average number of hours that all college freshmen spend watching TV per week

Question

To determine how many hours per week freshmen college students watch television, a random sample of 225 students was selected. It was determined that the students in the sample spent an average of 35 hours watching TV per week. The population standard deviation is known to be 12 hours. Provide a 95% confidence interval estimate for the average number of hours that all college freshmen spend watching TV per week

Answer 1

95% = mean ± 1.96 SEm

SEm = SD/√n

Insert values and calculate.

Answer 2

To calculate the confidence interval for the average number of hours that all college freshmen spend watching TV per week, we can use the formula:

Confidence interval = X̄ ± Z * (σ/√n)

Where:
X̄ = sample mean (35 hours)
Z = Z-score for the desired level of confidence (95% confidence corresponds to a Z-score of 1.96)
σ = population standard deviation (12 hours)
n = sample size (225 students)

Now let's plug in the values into the formula and calculate the confidence interval:

Confidence interval = 35 ± 1.96 * (12/√225)

Calculating √225 = 15

Confidence interval = 35 ± 1.96 * (12/15)

Calculating 12/15 = 0.8

Confidence interval = 35 ± 1.96 * 0.8

Calculating 1.96 * 0.8 = 1.568

Confidence interval = 35 ± 1.568

Lower bound = 35 - 1.568 = 33.432
Upper bound = 35 + 1.568 = 36.568

Therefore, the 95% confidence interval estimate for the average number of hours that all college freshmen spend watching TV per week is 33.432 to 36.568 hours.