A researcher selects a sample of 36 students from a school population with a mean IQ of 100 and 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?

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The null hypothesis is that the mean IQ in the sample is not significantly different from the population mean IQ of 100. The alternative hypothesis is that the mean IQ in the sample is significantly higher than the population mean IQ. With a one-sample z test at a .05 level of significance and a two-tailed test, the critical values for rejection are ±1.96. The test statistic is calculated as (104-100)/(12/√36) = 6, which is greater than 1.96. Therefore, we reject the null hypothesis and conclude that the mean IQ scores in the sample are significantly higher than those in the population.

A Researcher Selects a Sample of 36 Students from a School