Question

A social worker wants to find out whether the average IQ of a group of teenage prison inmates is below 100. The social worker assesses the IQ of a random sample of 38 inmates on a continuous scale. The mean IQ in this sample was 89 with a variance equal to 144. What is the appropriate anaylsis?

Answer 1

To determine whether the average IQ of teenage prison inmates is below 100, a social worker should perform a hypothesis test using a one-sample t-test. This involves stating the null and alternative hypotheses, calculating the test statistic, determining the critical value, and interpreting the results. If the null hypothesis is rejected, it can be concluded that the average IQ is below 100.

Step-by-step explanation:

Analysis of IQ Data

The appropriate analysis for the social worker is a hypothesis test to determine whether the average IQ of the teenage prison inmates is below 100. We can use a one-sample t-test to compare the sample mean with the hypothesized population mean. Here are the steps to perform this analysis:

1. State the null and alternative hypotheses:
   • Null hypothesis (H0): The mean IQ of the teenage prison inmates is equal to 100.
   • Alternative hypothesis (Ha): The mean IQ of the teenage prison inmates is less than 100.
2. Calculate the test statistic:
3. Determine the critical value and make a decision:
   • Using the t-distribution table or software, find the critical value for the chosen significance level (e.g., 0.05).
   • If the absolute value of the test statistic is greater than the critical value, reject the null hypothesis. Otherwise, fail to reject the null hypothesis.
4. Interpret the results:
   • If the null hypothesis is rejected, it can be concluded that the average IQ of the teenage prison inmates is below 100. Otherwise, there is not enough evidence to support the claim that the average IQ is below 100.