A researcher selects a sample of 36 students from a school population with a mean IQ of 100 and a standard deviation of 12.She determines that the mean IQ in this sample is 104.Assuming she computes a one-sample z test at a .05 level of significance,what is the decision for a two-tailed test?
A) Retain the null hypothesis; IQ scores in this sample are the same as those in the population.
B) Reject the null hypothesis; IQ scores in this sample are significantly higher than those in the population.
C) There is not enough information to make a decision.

Question

Quizplus · Accepted Answer

To determine the decision for the one-sample z test, we need to calculate the z-score:

z = (sample mean - population mean) / (standard deviation / square root of sample size)
z = (104 - 100) / (12 / sqrt(36))
z = 2

Since this is a two-tailed test, we need to look up the critical z-value at the .025 level of significance, which is 1.96 (using a z-table or calculator).

Since our calculated z-value of 2 is greater than the critical z-value of 1.96, we reject the null hypothesis. This means that there is evidence to suggest that the mean IQ score in the sample is significantly higher than the mean IQ score in the population.

A Researcher Selects a Sample of 36 Students from a School