Stats: Normal Distributions, Sample Means, and Null Hypotheses

1. To test Ho: μ=20 versus H1: μ<20, random sample size n=12 is obtained from a population that is known to be normally distributed with σ=2.
a. If the sample mean is determined to be 18.3, compute P-value.
b. If the researcher decides to test this hypothesis at the a=0.05 level of significance, will the researcher reject the null hypothesis?

2. Suppose you are using a=0.05 to test the claim that μ>16 using a P-value. You are given the sample statistics n=50 sample mean=16.3 and σ=1.2. find the P-value

3. To test Ho: μ= 105 versus H1: μ20 ≠105, a random sample size n=35 is obtained from a population that is known to be normally distributed with ơ= 12
a. Does the population need to be normally distributed to compute p-value?
b. If the sample mean is determined to be 100.7, compute P-value.
c. If the researcher decides to test this hypothesis at the α=0.02 level of significance , will the researcher reject the null hypothesis?

Solution Preview

1. a. z=(18.3-20)/(2/sqrt(12))=-2.94
P value=P(z<-2.94)=0.0016
b. Since P value is less than 0.05, the research will reject the null ...

Solution Summary

The solution determines the normal distributions, sample means, and null hypotheses.

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