Question

The Peabody Picture Vocabulary Test has a standard score population mean of 100 and standard deviation of 15. You tested a class of Grade 2 students wondering if their scores would be different from the population. After testing this hypothesis you decided to continue looking at this data to determine if there are any group differences based on birth order. You group the children based on whether they are the oldest the child, a middle child, or the youngest child. Here is the data based on the grouped information Oldest Child: 87 84 98 104 106 91 96 92 Middle Child: 65 74 62 60 73 64 71 78 Youngest Child: 115 84 85 83 95 94 108 102 89 Test the hypothesis at the 5% significance level (α = 0.05) using the 5-step hypothesis testing procedure (show ALL steps). Make sure to clearly state the null and alternative hypotheses in formal notation. Round all values to 2 decimal places.

Answer 1

To test the hypothesis that there are group differences based on birth order, we can use an ANOVA test.

Step-by-step explanation:

To test the hypothesis that there are group differences based on birth order, we can use an ANOVA (Analysis of Variance) test. This test allows us to compare the means of three or more groups. In this case, our three groups are the oldest child, the middle child, and the youngest child.

Step 1: State the null and alternative hypotheses:

H0 (Null Hypothesis): There is no difference in mean Peabody Picture Vocabulary Test scores among the three birth order groups.

HA (Alternative Hypothesis): There is a difference in mean Peabody Picture Vocabulary Test scores among the three birth order groups.

Step 2: Calculate the F statistic:

To calculate the F statistic, we need to calculate the between-group and within-group sum of squares.

Step 3: Determine the critical value:

We can use an F distribution table or a calculator to find the critical value for the given significance level (α = 0.05) and degrees of freedom.

Step 4: Compare the F statistic to the critical value:

If the calculated F statistic is greater than the critical value, we reject the null hypothesis and conclude that there is a significant difference in mean scores among the birth order groups.

Step 5: Make a conclusion:

Based on the calculated F statistic and the critical value, we can make a conclusion about whether there is a significant difference in mean scores among the birth order groups.