A sample of 65 night-school students' ages is obtained in order to estimate the mean age of night-school students. x bar = 25.2 years. The population variance is 28.
(a) Give a point estimate for ì. (Give your answer correct to one decimal place.)
Correct: Your answer is correct. .
(b) Find the 95% confidence interval for ì. (Give your answer correct to two decimal places.)
Lower Limit Incorrect: Your answer is incorrect. .
Upper Limit
(c) Find the 99% confidence interval for ì. (Give your answer correct to two decimal places.)
Lower Limit
Upper Limit
a. 25.2 years
b. Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability
(±.025) and its Z score.
95% = mean ± Z SEm
SEm = SD/√n
SD = √variance
c. Same process with ±.005.
(a) To obtain a point estimate for the mean age of night-school students (μ), we can use the sample mean (x̄). In this case, the sample mean is given as x̄ = 25.2 years. Therefore, the point estimate for μ is also 25.2 years.
(b) To find the 95% confidence interval for μ, we need to use the sample mean (x̄), the sample size (n), and the population variance (σ²).
The formula for the confidence interval is:
Confidence Interval = x̄ ± z * (σ / √n)
Here, x̄ = 25.2 (given), n = 65 (given), σ = √28 (population variance) = 5.29 (approximately).
To determine the z-value for a 95% confidence level, we refer to the Z-table or use a calculator. The z-value for a 95% confidence level is approximately 1.96.
Now, substituting the known values in the formula:
Confidence Interval = 25.2 ± 1.96 * (5.29 / √65)
Calculating this expression will give you the lower and upper limits of the 95% confidence interval for μ.
(c) To find the 99% confidence interval for μ, we follow the same steps as in part (b) but with a different z-value.
The z-value for a 99% confidence level is approximately 2.58. Using this value in the formula:
Confidence Interval = 25.2 ± 2.58 * (5.29 / √65)
Again, calculating this expression will provide you with the lower and upper limits of the 99% confidence interval for μ.