# Stats: Normal Distributions, Sample Means, and Null Hypotheses

1. To test Ho: Î¼=20 versus H1: Î¼<20, random sample size n=12 is obtained from a population that is known to be normally distributed with Ïƒ=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 Î¼>16 using a P-value. You are given the sample statistics n=50 sample mean=16.3 and Ïƒ=1.2. find the P-value

3. To test Ho: Î¼= 105 versus H1: Î¼20 â‰ 105, a random sample size n=35 is obtained from a population that is known to be normally distributed with Æ¡= 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 Î±=0.02 level of significance , will the researcher reject the null hypothesis?

https://brainmass.com/statistics/descriptive-statistics/stats-normal-distributions-sample-means-null-hypotheses-550660

#### 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.