6. A normally distributed population has a mean of 500 and a standard deviation

Question

6. A normally distributed population has a mean of 500 and a standard deviation of 100. A sample of 100 individuals is selected. a. Compute the mean of the distribution of sample means and the standard error of b. What is the probability of obtaining a sample with a mean as extreme as or more c. What is the probability of obtaining a sample mean as extreme as or more extreme d. If you are testing the null hypothesis Ho: H 500 with o .05, would you reject the mean. extreme than 530? than 470? or fail to reject the null hypothesis if you obtained a sample mean (M of 530?

Explanation / Answer

Ans:

Given that

mean=500

standard deviation=100

sample size,n=100

a)mean=500

standard error of mean=100/sqrt(100)=10

b)

z=(530-500)/10=3

P(z>=3)=0.0013

c)

z=(470-500)/10=-3

P(z>=-3)=0.9987

d)

p-value(2 tailed)=2*P(z>=3)=0.0026

As,p-value<0.05,we reject null hypothesis.

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