Confidence Interval Estimate of Mean with σ known?

2016-03-31 2:31 pm

The population mean can be estimated from a sample group with Z-score if either the standard deviation of the corresponding population is known or the sample size is large.

1. An analyst collected a simple random sample of n = 36 customers from a population of students of age 12, which gives the sample mean height of students as 125cm. It is known that the population standard deviation of height of students is 24cm.

a) Construct a 99 percent confidence interval for the population mean μ.

b) To interpret the interval, the analyst states that he has 99 percent confidence that the population mean height of students is between 114.7cm to 135.3cm. Explain the meaning of this statement.

I need the calculation steps, thank you very much!!!

回答 (1)

cidyah

2016-03-31 2:36 pm

✔ 最佳答案

a)
The critical z-value for a 99% confidence interval is 2.575
Sample mean = 125
Standard deviation = 24
Standard error of mean = σ / √ n
Standard error of mean = 24 / √ 36
SE = 24/6
Standard error of mean 4
Confidence interval 125-(4)(2.575) and 125+(4)(2.575)

(114.7, 135.3)

b)
It means if repeated sampling was used and a confidence interval constructed for each sample, 99 percent of these samples would enclose the true population mean.

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