Question #347851

1) If a hypothesis is conducted using 𝐠= 0.05, for which of the following p-values would the null hypothesis be rejected?


2) For each pair of ? and p-value, indicate whether the null hypothesis would be rejected.


3) In a test of H₀: µ = 80 against H₁: µ<80, the sample data yielded the test statistic z = 1.63. What is


the p-value for the test?


4) In a test of H₀: µ = 80 against H₁: µ ≠ 80, a sample of observations had a mean and standard


deviation s = 4.1. What is the p-value for this test?


5) In a test of H₀: µ = 72 against H₁: µ ≠ 72, the sample data yielded the test statistic z = 1.63. Find the p-value for the test.

1
Expert's answer
2022-06-07T19:13:19-0400

1)

e) 0.001


2)

a) p=0.10>0.05=α,p=0.10>0.05=\alpha, don't reject

b) p=0.05=0.05=α,p=0.05=0.05=\alpha, don't reject

c) p=0.001<0.01=α,p=0.001<0.01=\alpha, reject

d) p=0.10>0.01=α,p=0.10>0.01=\alpha, don't reject

e) p=0.01<0.10=α,p=0.01<0.10=\alpha, reject


3)

Left-tailed test p=P(Z<1.63)=0.948449p=P(Z<1.63)=0.948449


4)

This corresponds to a two-tailed test, for which a t-test for one mean, with unknown population standard deviation, using the sample standard deviation, will be used.

The t-statistic is computed as follows:


t=xˉμs/nt=\dfrac{\bar{x}-\mu}{s/\sqrt{n}}


The p-value for two-tailed, df=n1df=n-1 degrees of freedom, t=xˉμs/nt=\dfrac{\bar{x}-\mu}{s/\sqrt{n}} can be defined if xˉ,μ,s,n\bar{x}, \mu, s, n are given.


5)

Two-tailed test p=2P(Z>1.63)=0.103101p=2P(Z>1.63)=0.103101



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