---
tags: 機率與統計
title: 第十週活動
---

# 活動一

#### (a) Would a 90% confidence interval calculated from this same simple have been narrower or wider than the given interval? Explain your reasoning.
ans:90%會更窄，因為表示說只會有90%的產品符合條件

#### (b) Consider the following statement: There is a 95% chance that u is between 7.8 and 9.4. Is this statement correct? Why or why not?
ans:不正確，應該是說如果今天隨機抽樣，樣本在這個範圍間的機率為95%

#### (c) Consider the following statement: We can be highly confident that 95% of all bottles of this type of cough syrup have an alcohol content that is between 7.8 and 9.4. Is the statement correct? Why or why not?
ans:不正確，因為95%只是代表從樣本推估母體中符合條件的總共會有95%，並不等於一定是95%都在這個範圍

#### (d) Consider the following statement: If the process of selecting a sample of size 50 and then computing the corresponding 95% interval is repeated 100 times, 95 of the resulting intervals will include u. Is this statement correct? Why or why not
ans:不正確，因為不可能會剛好為95個，95%的意思是指說在無窮大的情況下比率會接近95%，所以不可能出現100個中剛好有95個

# 活動二

TV advertising agencies face growing challenges in reaching audience members because viewing TV programs via digital streaming is increasingly popular. The Harris poll reported on November 13, 2012, that 53% of 2343 American adults surveyed said they have watched digitally streamed TV programming on some type of device.

#### (a) Calculate and interpret a confidence interval at the 99% confidence level for the proportion of all adult Americans who have watched streamed programming.

#### (b) What sample size would be required for the width of a 99% CI to be at most .05 irrespective of the value of p?