A random sample of 20 people who resided within the u.s resulted in average viewing time of 4.76 hrs per day with a sample standard deviation of 2.297 hrs. obtain and interpret a 95% confidence interval, for the mean viewing time of all americans

confidence interval:
Interpert your answer:

95% = mean ± 1.96 SEm

SEm = SD/√n

I'll let you interpret.

To obtain a 95% confidence interval for the mean viewing time of all Americans, we can use the formula:

Confidence Interval = Sample Mean +/- (Critical Value * Standard Error of the Mean)

First, we need to find the critical value. Since we are using a 95% confidence level, the corresponding critical value can be found in the Z-table. In this case, the critical value is 1.96.

Next, we need to calculate the standard error of the mean. This can be done using the formula:

Standard Error of the Mean = Sample Standard Deviation / √(Sample Size)

Plugging in the values, we have:

Standard Error of the Mean = 2.297 / √20 ≈ 0.514

Now, we can calculate the confidence interval:

Confidence Interval = 4.76 ± (1.96 * 0.514)
Confidence Interval = 4.76 ± 1.008
Confidence Interval = (3.752, 5.768)

Interpreting the confidence interval, we can say with 95% confidence that the mean viewing time of all Americans falls within the range of 3.752 to 5.768 hours per day.