Question

A professor at a small college suspects that poor readers may test lower in IQ than those whose reading is “satisfactory.” (Possibly AT grade level?) She draws a random sample of 28 students who are labeled as “poor readers.” She examines the data in the historical archives and finds a population mean IQ of 105. The sample of 28 has a mean of 103.8 with a sample standard deviation of 1.42. Again using a level of significance of 0.05, test the hypothesis that the IQ is lower. State the Null/Alternate Hypothesis 1- or 2- Tails? Sketch an initial picture Level of Significance z- or t- tests? Why??? List the Test Statistic (e.g., the formula you will use) Formulate the Decision Rule (use a picture) (use Level of Significance) (Use the z- or t- critical value) (Then state the Decision Rule!!!) Run the actual data through the Test Statistic and make a Decision based on the rule!!! Interpret the Result Find the p-value

Answer 1

Null Hypothesis

ALternative Hypothesis (Left tailed)

Since population standard deviation is unknown , we use t- distribution

Under H0, the test statistic is

Degrees of freedom = n-1= 28-1=27

The critical value of t for 27 df at 5% significance level is -1.703

Decision Rule : Reject H0. if t <-1.703

The P-Value is 0.000063

Since p value is less than significance level, REject H0.

Hence at 5% significance level we have evidence to support the claim that poor readers may test lower in IQ than those whose reading is “satisfactory.”