Question

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

6,38,13,4,34,38,20,15,19,29,14,54

estimate with 93% confidence the mean number of rounds played per year by physicians, assuming that the population is normally distributed with a standard deviation of 7.

Answer 1

To estimate the mean number of rounds played per year by physicians, we can use the sample data provided and assume that the population is normally distributed with a standard deviation of 7. Using a z-test at a 93% confidence level, the estimated mean number of rounds played per year by physicians is between 15.17 and 22.49.

Step-by-step explanation:

To estimate the mean number of rounds played per year by physicians, we can use the sample data provided and assume that the population is normally distributed with a standard deviation of 7. Since the sample data is small (n = 12) and the population standard deviation is known, we can use a z-test to estimate the mean with a 93% confidence level.

1. Calculate the sample mean: sum of the numbers / sample size = (6 + 38 + 13 + 4 + 34 + 38 + 20 + 15 + 19 + 29 + 14 + 54) / 12 = 18.83 (rounded to two decimal places)
2. Calculate the standard error: population standard deviation / square root of the sample size = 7 / sqrt(12) = 2.02 (rounded to two decimal places)
3. Find the critical z-value for a 93% confidence level: look up the z-value for a confidence level of 93% in a standard normal distribution table or use statistical software, which is approximately 1.81 (rounded to two decimal places).
4. Calculate the margin of error: critical z-value * standard error = 1.81 * 2.02 = 3.66 (rounded to two decimal places)
5. Calculate the confidence interval: sample mean ± margin of error = 18.83 ± 3.66 = (15.17, 22.49) (rounded to two decimal places)

Therefore, we can estimate with 93% confidence that the mean number of rounds played per year by physicians is between 15.17 and 22.49.