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李丰丰 · 2020年02月20日

问一道题:NO.PZ2020010304000049 [ FRM I ]

问题如下:

Find the p-value for the following t-test statistics of the null hypothesis, H0:μ=μ0H_0: \mu = \mu_0.

a. Statistic: 1.45, Alternative: Two-sided

b. Statistic: 1.45, Alternative: One-sided upper

c. Statistic: 1.45, Alternative: One-sided lower

d. Statistic: -2.3, Alternative: One-sided upper

e. Statistic: 2.7, Alternative: Two-sided

解释:

a. In a two-sided test, the p-value is the area under the normal curve for values greater than 1.45 or less than -1.45. This is twice the area less than -1.45, or 2 * 0.074. = .148.

b. In a one-sided upper test, we need the area above 1.45. This is half the previous answer, or 0.074.

c. In a one-sided lower test, we need the area under the curve for values less than 1.45. This is just 1 - 0.074 = .926.

d. Here we need to probability under the normal curve for values above -2.3, which is 1 minus the area less than -2.3, or 1 - 0.01 = 0.99.

e. Because it is a two-sided alternative, we need that area for values larger than 2.7 or less than -2.7, which is twice the area less than -2.7. This value is 2 * .0034 = .0068.

您好,请问怎么从statistic推算出p-value呢?0.074是如何得到的呢?答案有些不理解,谢谢
1 个答案

品职答疑小助手雍 · 2020年02月20日

同学你好,题目条件给的一点几,二点几都是标准差的倍数,你需要通过查表找到这些标准差倍数对应的累计概率

问的是拒绝域的百分比,拿a举例,问的其实是距离均值1.45倍标准差之外的概率占多少。

查表出来的是累计概率那双边的话就用1减查表的累计概率,再乘以2就得到拒绝域概率占比了。

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