A sample of 230 observations is selected from a normal population with a population standard deviation of 26. The sample mean is 18. (Use t Distribution Table & z Distribution Table.)
Question
A sample of 230 observations is selected from a normal population with a population standard deviation of 26. The sample mean is 18. (Use t Distribution Table & z Distribution Table.)
Solution
You didn't specify a question, but I'm assuming you want to calculate the confidence interval for the population mean. Here's how you can do it:
- Identify a sample size or number of observations: n = 230
- Identify a standard deviation or standard error: σ = 26
- Identify a sample mean: x̄ = 18
Since the sample size is large (n > 30), we can use the z-distribution to calculate the confidence interval.
-
Choose your desired confidence level. For example, if you want a 95% confidence level, the z-value from the z-distribution table is 1.96.
-
Calculate the standard error of the mean (SE). SE = σ/√n = 26/√230 ≈ 1.71
-
Calculate the margin of error (E). E = z * SE = 1.96 * 1.71 ≈ 3.35
-
Calculate the confidence interval. The lower limit is x̄ - E = 18 - 3.35 = 14.65 and the upper limit is x̄ + E = 18 + 3.35 = 21.35.
So, the 95% confidence interval for the population mean is (14.65, 21.35).
Similar Questions
A sample of 230 observations is selected from a normal population with a population standard deviation of 26. The sample mean is 18. (Use t Distribution Table & z Distribution Table.)Required:a. Determine the standard error of the mean. (Round your answer to 3 decimal places.)c. Determine the 99% confidence interval for the population mean. (Round your answers to 3 decimal places.)
Given the following values 25, 7, 22, 33, 18, 15The population mean and population standard deviation are approximately:
A sample of 39 observations is selected from a normal population. The sample mean is 43, and the population standard deviation is 6. Conduct the following test of hypothesis using the 0.02 significance level.
The s.d. of the sampling distribution of sample mean for the population with s.d. 0.5, population size 122 and sample size 22 is
The mean of 25 observations is 36. Out of these observations if the mean of first 13 observations is 32 and that of the last 13 observations is 40, the 13th observation is
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.