Archie H 發問時間： 科學數學 · 7 年前

# 【急，統計問題】徵求統計高手解題

A matched pairs experiment compares the taste of instant versus fresh-brewed coffee. Each subject tastes two unmarked cups of coffee, one of each type, in random order and states which he or she prefers. Of the 40 subjects who participate in the study, 12 prefer the instant coffee. Let p be the probability that a randomly chosen subject prefers fresh-brewed coffee to instant coffee. (In practical terms, p is the proportion of the population who prefer fresh-brewed coffee.)

(a)Test the claim that a majority of people prefer the taste of fresh-brewed coffee. Report the large-sample z statistic and its p-value.

(b)Draw a sketch of a standard Normal curve and mark the location of your z statistic. Shade the appropriate area that corresponds to the p-value.

(c)Is your result significant at the 5% level? What is your practical conclusion?

### 13 個解答

• 7 年前
最佳解答

This is an either or situation. Since you could only have one or the other. So since it is a large sample and it falls within the 95% probability, you can state with a fair degree of accuracy that "Most people prefer fresh brewed coffee as opposed to instant"

參考資料： kon
• 7 年前

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• 7 年前

這是一個基本的二項比例假說檢定問題.

n=40, x=28 (樣本中12人偏愛 instant coffee, 也就是說28人偏愛

fresh-brewed coffee).

(a) 要檢定 the claim that a majority of people prefer the taste of

fresh-brewed coffee, 即 對立假說 Ha 為 p > 1/2. 相對地,

虛無假說 H0 是 p < or = 1/2.

2014-04-12 19:04:12 補充：

題目中說明用大樣本方法, 即用常態近似.

z = [28-40*(1/2)]/√[40*(1/2)(1-1/2)] = 8/√10 = 2.53

p-value = P[ Z >= z ] =0.0057

(c) p-value < 顯著水準, 所以是顯著的. 也就是說, 這實驗結果

證實了 "大部分人較偏愛 fresh-brewed coffee" 的說法.