Question

A citizen claims that the intelligence of children in a particular community is below average. To test this claim, he selects a simple random sample consisting n=10 children from this population. Score of the intelligence test typically normally distributed with a population mean 100 and a standard deviation 15. The sample mean is 98. We want to test whether the intelligence score of children in this community was significantly less than 100 (one-sided) at 95% confidence level. Assuming that the p-value is 0.3372, what is your conclusion ?

Answer 1

solution:

the given data as follows:

sample size = n = 10

sample mean =

population standard deviation is

we have to test whether the claim that intelligence is below the average of 100

so null and alternative hypothesis:

since population standard deviation is known so we use z - distribution

confidence level = 95% = 0.95

significance level = = 1-0.95 = 0.05

test statistics:

p value = value of z to the left if -0.42 = 0.3372

since p value 0.3372 > = 0.05, so do not rejecting the nul hypothesis

conclusion:

it is concluded that there is not enough evidence to support the claim than mean interlligence of children is less than 100.