Question

(1 point)

How many rounds of golf do those physicians who play golf play per year? A survey of 12 physicians revealed the following numbers:

6,42,18,1,35,42,22,16,16,25,11,54
Estimate with 95% confidence the mean number of rounds played per year by physicians, assuming that the population is normally distributed with a standard deviation of 6.

Note: For each confidence interval, enter your answer in the form (LCL, UCL). You must include the parentheses and the comma between the confidence limits.

Confidence Interval =

Answer 1

The estimated mean number of rounds of golf played per year by physicians is between 20.606 and 27.394, with 95% confidence.

Step-by-step explanation:

To estimate the mean number of rounds of golf played per year by physicians with 95% confidence, we will use the sample mean (×-bar) and the population standard deviation (σ) to find the confidence interval (CI). First, we calculate the sample mean:

1. Add up all the sample values: 6 + 42 + 18 + 1 + 35 + 42 + 22 + 16 + 16 + 25 + 11 + 54 = 288 rounds.
2. Divide the total by the number of physicians (n): 288/12 = 24 rounds.

Now, since the population standard deviation is known (σ = 6) and the sample size (n = 12) is less than 30, we'll use the Z-distribution to find the Z-score for 95% confidence. The Z-score corresponding to 95% confidence is approximately 1.96 (found in Z-tables or standard normal distribution).

The formula for the CI is:

CI = ×-bar ± Z * (σ/√n)

Plugging in the values:

CI = 24 ± 1.96 * (6/√12)

Calculate the margin of error:

Margin of Error = 1.96 * (6/3.4641) = 1.96 * 1.732 = approximately 3.394

Finally, the 95% CI is:

CI = (24 - 3.394, 24 + 3.394)

CI = (20.606, 27.394)