statistic 問題

a) Estimate the population?
Estimate what of the population?
If it's mean, it's your best guess: 60 lb.
If it's standard error, it's 20/sqrt(16) = 5 lb.

b) Explain why we need to use t distribution. what assumption do you need to make
t-distribution is needed because when sample size is small (usually 30 or less), the sample means do not follow normal distribution, but t-distribution. So, t-distribution should be used in order to avoid inflated type I error (false rejection of the null hypothesis).

Assumptions for estimating the population mean:
- The sampling is random
- The individuals in the sample show a normal distribution
- The samples are independent from each other (one man's sugar consumption should not affect the other's sugar consumption)
(This one is usually implied, but good to mention: measurement errors are either random or negligible)

c) Develop the 90% confidence interval for he population mean
Standard error = 5 lb
Mean = 60 lb
Check the table, percentile z-score of t-distribution with 5% at both tails is +/- 1.746.
90% CI = 60 +/- 1.746(5)
= 51.27, 68.73

2007-04-11 05:00:06 補充：
Correction:1.746 in part (c) should be 1.753. I used degree of freedom = 16, that was a mistake. the df should be 15 (n-1 for the mean) only. So, 1.753 is the right number:90% CI = 60 +/- 1.753(5)= 51.23 lb, 68.77 lb