­»¯ó V 發問時間: 社會與文化語言 · 1 0 年前

統計關於Null- hypotheses

You are given the following information obtained from a random sample of 5 observations. Assume the population has a normal distribution.

20-----------18------------17------------22------------18

You want to determine whether or not the mean of the population from which this sample was taken is significantly less than 21.

a.State the null and the alternative hypotheses.

b.Compute the standard error of the mean.

c.Determine the test statistic.

d.Determine the p-value and at 90% confidence, test whether or not the mean of the population is significantly less than 21.

已更新項目:

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1 個解答

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  • 阿泰
    Lv 6
    1 0 年前
    最佳解答

    a.

    H0: 母體平均數>=21 v.s. Ha: 母體平均數<21

    b.

    Xbar=[20+18+17+22+18]/5=19

    Sx2=[(20-19)2+(18-19)2+(17-19)2+(22-19)2+(18-19)2]/[5-1]=4

    The standard error of the mean

    =根號{Sx2/n}=根號{4/5}=0.8944

    c.Determine the test statistic.

    檢定統計量T=[Xbar-21]/根號{Sx2/n}=[19-21]/根號{4/5}= -2.236

    d.

    P-value=P(T(4)>|-2.236|=2.236),查自由度為4的t分配表,t分配大於2.236的機率為0.0445,因此P-value=P(T(4)>2.236)=0.0445。

    又90的信心,表示顯著水準alpha=0.1,P值=0.0445<0.1,故拒絕H0,表示母體平均數小於21。

    因為母體標準差未知,且樣本又不夠大,因此此題不能長Z分配表,而是查t分配表,自由度為n-1=4。

    參考資料: 總是認真回答每個問題的自己
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