A study was conducted in order to estimate u, the mean number of weekly hours that U.S. adults use computers at home. Suppose a random sample of 81 U.S. adults give a mean weekly computer usage time of 8.5 hours and that from prior studies , the population standard deviation is assumed to be 3.6 hours.
Are you looking for the confidence interval?
What level of significance are you using?
95% = mean ± 1.96 SEm
SEm = SD/√n
n a planned study, there is a known population with a normal disrubution, \mu= 0, and \sigma=10. What is the predicted effect size (d) if the researchers predict that those given an experimental treatment have a mean of (a) -8, (b) -5, (c) -2, (d) 0, and (e) 10 ? For each part, also indicate wether the effect is approximatley small, medium, or large.
To estimate the mean number of weekly hours that U.S. adults use computers at home (u), a study was conducted with a sample of 81 U.S. adults. The sample mean weekly computer usage time was found to be 8.5 hours, and the population standard deviation, based on prior studies, is assumed to be 3.6 hours.
To better understand the estimation process, we can use the formula for calculating the confidence interval for a population mean. The confidence interval provides a range of values within which we can reasonably expect the true population mean to fall.
The formula for the confidence interval is:
CI = x̄ ± z * (σ/√n)
Where:
CI represents the confidence interval,
x̄ is the sample mean (8.5 hours),
z is the z-value representing the desired level of confidence (e.g., 95% confidence level corresponds to a z-value of 1.96 for a large sample),
σ is the population standard deviation (3.6 hours), and
n is the sample size (81).
Let's assume we want to calculate a 95% confidence interval for the true mean number of weekly computer usage hours.
Step 1: Find the z-value
To find the appropriate z-value for a 95% confidence level, we can refer to the standard normal distribution table or use statistical software. A 95% confidence level corresponds to a z-value of approximately 1.96.
Step 2: Calculate the margin of error
The margin of error is determined by multiplying the z-value with the standard error, which is the population standard deviation (σ) divided by the square root of the sample size (√n). In this case:
Margin of error = z * (σ/√n)
= 1.96 * (3.6/√81)
≈ 0.78
Step 3: Calculate the confidence interval
Using the formula for the confidence interval:
CI = x̄ ± margin of error
= 8.5 ± 0.78
= (7.72, 9.28)
Therefore, we can state with 95% confidence that the true mean number of weekly computer usage hours for U.S. adults falls within the interval of 7.72 to 9.28 hours.