confidence interval

[匿名]

2007-05-22 3:57 pm

A sample of 64 tires lasts for a mean of 39500 miles.It is known that the standard deviation for this type of tire is 4400 miles.

a) How would the length of the confidence interval be effected if the same information were obtained from a sample of 200?

b) If the manufacturer claims that these tires last for 40000 miles, would you accept that claim? Explain your answer.

請詳細地解釋每題答案和列出計算步驟!!! thx

回答 (1)

The Little Prince of Mathematics

2007-05-22 5:48 pm

✔ 最佳答案

a)
The length of the confidence inteval: 2* A-1(x) * 4400 / [sqrt n]
where A-1(x) is the inverse of normal distribution and n is the sample size.

Assume A-1(x) will not change,
The larger the n, the shorter the length.

Therefore length of confidence interval will be shortened.

b)
Z = (39500-40000)/(4400/[sqrt 64]) = -10/11
Usually, in this case, whenever you use a 90% confidence inteval or 95% confidence inteval, you should accept the hypothesis by the manufacturer.
Therefore, these tires can last for 40000 miles.

參考: me

👍 0 👎 0