A random sample of 100 cable TV movies contained an average of 3.38 acts of physical violence per program. At the 99% level what is your estimate of the population value?

mean = 3.38
s = 0.30
N = 100

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability (.005) and its Z score.

99% = mean ± Z * SEm

SEm = SD/√n = s/√N

0.019

To estimate the population value at the 99% level, we can use the formula for the confidence interval.

The formula for the confidence interval is:

CI = X̄ ± Z * (σ/√n)

where:
CI = Confidence Interval
X̄ = Sample Mean
Z = Z-score for the desired confidence level (99% confidence level corresponds to a Z-score of 2.576)
σ = Population Standard Deviation
n = Sample Size

In this case, we have:
X̄ = 3.38
Z = 2.576
σ = 0.30
n = 100

Plugging in the values into the formula, we get:

CI = 3.38 ± 2.576 * (0.30/√100)

Simplifying:

CI = 3.38 ± 2.576 * 0.03

CI = 3.38 ± 0.07728

Calculating the upper and lower limits:

Upper Limit = 3.38 + 0.07728
Upper Limit = 3.45728

Lower Limit = 3.38 - 0.07728
Lower Limit = 3.30272

Therefore, at the 99% level, our estimate of the population value is between 3.30272 and 3.45728 acts of physical violence per program.

To estimate the population value at the 99% confidence level, you can use the formula for the margin of error and then calculate the confidence interval.

The formula for the margin of error is given by:

Margin of Error = Critical Value * Standard Error

The critical value depends on the desired confidence level. At a 99% confidence level, the critical value is obtained from the t-distribution with 99 degrees of freedom. For a two-tailed test, the critical value is approximately 2.626.

The standard error is given by the formula:

Standard Error = Standard Deviation / sqrt(sample size)

In this case, the sample size (N) is 100 and the standard deviation (s) is 0.30.

Using these values, we can calculate the standard error:

Standard Error = 0.30 / sqrt(100)
= 0.30 / 10
= 0.03

Now, we can calculate the margin of error:

Margin of Error = 2.626 * 0.03
= 0.0788

Finally, the confidence interval can be calculated as:

Confidence Interval = Sample Mean +/- Margin of Error

Sample Mean = 3.38

Confidence Interval = 3.38 +/- 0.0788
= (3.3012, 3.4588)

Therefore, at the 99% confidence level, the estimated population value is between 3.3012 and 3.4588 acts of physical violence per program.