8. A normally distributed population has a sample of 100 individuals is selected

Question

8. A normally distributed population has a sample of 100 individuals is selected. a. Compute the mean of the distribution of sample means and the standard error of the mean. mean of 50 and a standard deviation of 10, A b. What is the probability of obtaining a sample with a mean as extreme as or more extreme than 51? What is the probability of obtaining a sample mean as extreme as or more extreme c. than 48? d. If you are testing the null hypothesis Ho: H 50 with a or fail to reject the null hypothesis if you obtained a sample mean (M) of 48? .01, would you reject

Explanation / Answer

8.
mean = 50
sd = 10
n = 100

a)
mean = 50
std. error = sd/sqrt(n) = 10/sqrt(100) = 1

b)
P(X >= 51)
= P(z >= (51 - 50)/1)
= P(z >= 1)
= 0.1587 .. using standard z table

c)
P(X >= 48)
= P(z >= (48 - 50)/1)
= P(z >= -2)
= 0.9772 .. using standard z table

d)
For sample mean of 48
test statistics, z = (48 - 50)/1 = -2

p-value = 0.0228 ... (using standard z table)

As p-value is greater than the significance level of 0.01, we fail to reject the null hypothesis.

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