Question

The amount of television viewed by​ today's youth is of primary concern to a certain organization. three hundred parents of elementary​ school-aged children were asked to estimate the number of hours per week that their child watched television. the mean and the standard deviation for their responses were 1919 and 44​, respectively. the organization constructed a​ stem-and-leaf display for the data that showed that the distribution of times was a bell shaped distribution. give an interval around the mean where most​ (approximately 95%) of the television viewing times fell in the distribution

Answer 1

The interval around the mean is 18.55 ≤ μ ≤ 19.45

We follow these steps to arrive at the answer above:

Confidence level : 95%

Confidence Interval Estimate: Sample mean ± t_n-1* (s/√n)

Critical t value at n-1 df (300-1 = 299 d.f) is 1.96793

Substituting values in the formula above we get,

Confidence Interval Estimate = 19± 1.96793 (4/√300)

Confidence Interval Estimate = 19 ± 0.454473966