Answer :
(a) The point estimate of µ (population mean) is 14, calculated as the sample mean. (b) The 99% confidence interval for µ is approximately (-31.29, 59.29) based on the sample data and standard deviation.
To calculate the point estimate of µ (the population mean) and the boundaries of the 99% confidence interval for µ, we can use the sample data and the given standard deviation.
(a) Point Estimate of µ:
The point estimate of µ is the sample mean (x), which is calculated as the sum of the data values divided by the number of data points:
x = (18 + 13 + 12 + 15 + 12) / 5 = 70 / 5 = 14
So, the point estimate of µ is 14.
(b) Confidence Interval for µ:
To calculate the boundaries of the 99% confidence interval for µ, we can use the formula:
Confidence Interval = x ± Z * (σ / √n)
Where:
x is the sample mean (14 in this case).
Z is the critical value for a 99% confidence interval. You can find this value using a standard normal distribution table or calculator. For a 99% confidence interval, Z ≈ 2.576 (approximately).
σ is the population standard deviation, but in this case, we are given the sample standard deviation, so we'll use it (σ ≈ 47.8).
n is the sample size (5 in this case).
Now, calculate the confidence interval:
Confidence Interval = 14 ± 2.576 * (47.8 / √5)
Confidence Interval ≈ 14 ± 2.576 * (47.8 / √5)
Confidence Interval ≈ 14 ± 45.29
The boundaries of the 99% confidence interval for µ are approximately:
Lower Boundary ≈ 14 - 45.29 ≈ -31.29
Upper Boundary ≈ 14 + 45.29 ≈ 59.29
So, the 99% confidence interval for µ is approximately (-31.29, 59.29).
To know more about standard deviation:
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