Question

the accompanying table shows the ages (in years) of 11 children and the numbers of words in their vocabulary. complete parts (a) through (d) below. click here to view the data table. click here to view the table of critical values for the pearson correlation coefficient. as age increases, the number of words in childrens vocabulary tends to increase. (d) use the table of critical values for the pearson correlation coefficient to make a conclusion about the correlation coefficient. let α = 0.01. the critical value is . therefore, there sufficient evidence at the 1% level of significance to conclude that between childrens ages and the number of words in their vocabulary. (round to three decimal places as needed.)

Explanation:

Step1: Determine degrees of freedom

The number of data - points $n = 11$. The degrees of freedom $df=n - 2=11 - 2 = 9$.

Step2: Find critical value

For a two - tailed test with $\alpha=0.01$ and $df = 9$, looking up in the critical - values table for the Pearson correlation coefficient, the critical value is $r_{c}=0.735$.

Step3: Make conclusion

If the absolute value of the calculated Pearson correlation coefficient $|r|$ is greater than the critical value $r_{c}$, there is a significant correlation. If $|r|\leq r_{c}$, there is not a significant correlation. Since we don't have the calculated $r$ value here, but just the critical - value part of the problem, we state the critical value.

Answer:

The critical value is $0.735$. There is not enough information given in the problem to determine if there is sufficient evidence (we would need the calculated correlation coefficient to make that determination).