Confidence Interval Estimate of Mean with σ Unknown?

2016-03-27 3:37 pm

Usually, the standard deviation of population is unknown. To determine the confidence interval estimation, t distribution will be adopted.

b) To estimate the average price of wine produced in year 2013, a sample of 17 wines of year 2013 is selected. The mean and standard deviation of the prices of the sampled wines USD34.59 and USD9.894 respectively.
i) Construct a 98 percent confidence interval for the population mean price of the wine in year 2013.

ii) Suppose that a wine cellar keeps an inventory of 300 wines of year 2013. By using the interval in b)i), estimate the range of total prices of the 300 wines.

iii) In order to construct the confidence interval estimate in b)i), what extra assumption must be made?

THANK YOU VERY MUCH

回答 (1)

cidyah

2016-03-27 4:42 pm

✔ 最佳答案

b)
i)
The critical t (with 16 degrees of freedom) for 98% confidence interval is 2.5835
Sample mean = 34.59
Standard deviation = 9.894
Standard error of mean = s / √ n
Standard error of mean = 9.894 / √ 17
SE = 9.894/4.1231
Standard error of mean 2.3996
Confidence interval 34.59-(2.3996)(2.5835) and 34.59+(2.3996)(2.5835)

(28.39, 40.79)

ii)
(300*28.39, 300*40.79)
= ($8,517, $120,237)

iii)
The sample comes from a normal population. Random sampling was used.

👍 0 👎 0