A simple random sample of size 15 has mean x=14.3 and the standard deviation is s=2.45. The population is not approximately normal. Can you conclude that the population mean is less than 10?

Question

The population standard deviation [is or isnt?] known.
The sample size n [is or isnt] greater than 30.
The population [is or is not?] approximately normal.
The correct decision is to [perform the z-test, perform the t-test or consult to a statistician?]

Answer 1

To address your questions step-by-step:

1. Population Standard Deviation: The population standard deviation is not known. Since you provided the sample standard deviation (s = 2.45), we can conclude that the population standard deviation is not known.

2. Sample Size: The sample size \( n = 15 \) is not greater than 30.

3. Population Normality: The population is not approximately normal, as stated in your question.

4. Correct Decision for Testing: Given that the population standard deviation is not known, the sample size is less than 30, and the population is not approximately normal, the correct decision is to consult to a statistician. Since the sample size is small and the normality assumption is violated, traditional hypothesis tests (such as t-tests or z-tests) may not be appropriate.

In summary:

• Population standard deviation: not known
• Sample size: not greater than 30
• Population normality: not approximately normal
• Correct decision: consult to a statistician