Question

The mean population IQ is 100 with a standard deviation of 15. A principal at a certain school claims that the mean IQ score of their students in his school is greater that 100. A random sample of 30 students IQ scores have a mean score of 112. Significance level α = 0.01

(a) State the null and alternate hypotheses

(b) Calculate the z statistic value 6

(c) Determine the p value. Sketch the graph

(d) Make a decision. Reject or fail to reject H0 ?

(e) Is there sufficient evidence at the 1% significance level to support the principal’s claim? Explain your answer in relation to this context.

Answer 1

solution:

the given data as follows:

sample size = n = 30

sample mean =

population standard deviation:

a) null and alternative hypothesis:

since population standard deviation is know so we will use the z test statistics:

b) test statistics:

c) p value = 1 - value of z to the left of 4.38 = 1 - 0.999999 = 0.000001

p value is 0.000001

significance level = = 0.01

since p value 0.00001 < = 0.01, so reject the null hypothesis

conclusion:

there is sufficient evidence to support the claim that the average IQ score of students is greater than 100.

c)

\alpha = 0.10, since p value < 0.1, so rejecting the null hypothesis

concluded that the mean distance is differ from the 120 feet.