A simple random sample of 50 adults was surveyed, and it was found that the mean amount of time that they spend surfing the Internet per day is 54.2 minutes, with a standard deviation of 14.0 minutes. What is the 99% confidence interval for the number of minutes that an adult spends surfing the Internet per day?

To calculate the 99% confidence interval for the number of minutes that an adult spends surfing the Internet per day, we can use the formula:

Confidence interval = mean ± (critical value * standard error)

First, we need to determine the critical value. Since the sample size is relatively large (n > 30), we can use the Z-distribution.

For a 99% confidence level, the critical value can be found using a standard normal distribution table or a calculator. The critical value for a 99% confidence level is approximately 2.576.

Next, we need to calculate the standard error, which measures the variability of the sample mean. The formula for the standard error is:

Standard error = standard deviation / √sample size

Given that the standard deviation is 14.0 minutes and the sample size is 50, we can calculate the standard error as follows:

Standard error = 14.0 / √50 ≈ 1.98

Now, we can plug in the values into the confidence interval formula:

Confidence interval = 54.2 ± (2.576 * 1.98)

Calculating the upper bound:

Upper bound = 54.2 + (2.576 * 1.98) ≈ 54.2 + 5.1 ≈ 59.3

Calculating the lower bound:

Lower bound = 54.2 - (2.576 * 1.98) ≈ 54.2 - 5.1 ≈ 49.1

Therefore, the 99% confidence interval for the number of minutes that an adult spends surfing the Internet per day is approximately 49.1 to 59.3 minutes.

To calculate the confidence interval, we can use the following formula:

Confidence Interval = sample mean ± (critical value x standard deviation / square root of sample size)

1. First, let's find the critical value. Since we want a 99% confidence interval, we need to find the Z-score associated with a 99% confidence level.

The confidence level of 99% corresponds to an alpha level of 0.01 (1 - 0.99 = 0.01). We can find the Z-score using a standard normal distribution table or calculator, which gives us a Z-score of approximately 2.576.

2. Now, we can substitute the values from the problem into the formula:

Confidence Interval = 54.2 ± (2.576 x 14.0 / √50)

3. Next, we calculate the standard error, which is the standard deviation divided by the square root of the sample size:

Standard Error = 14.0 / √50

4. Finally, we substitute the standard error into the formula:

Confidence Interval = 54.2 ± (2.576 x Standard Error)

Calculating the value:

Standard Error ≈ 14.0 / √50 ≈ 1.98

Confidence Interval = 54.2 ± (2.576 x 1.98)

Using a calculator:

Confidence Interval ≈ 54.2 ± 5.1

Therefore, the 99% confidence interval for the number of minutes that an adult spends surfing the Internet per day is approximately 49.1 to 59.3 minutes.

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 = 2.575.

99% = mean ± 2.575 SEm

SEm = SD/√n