A pediatrician wants to know if there is a correlation between the ages of children and the number of vocabulary words they can say. The following table lists the ages and number of vocabulary words of six randomly selected children.

Ages of children (in months)	13	14	15	16	16	18
Number of vocabulary words	8	10	15	20	27	30

a. (9 points)

The sample correlation r is 0.948.

Test the correlation coefficient using 0.05 as the significance level.

H₀ :

H₁ :

Critical number(s) =

Round the same as the critical number(s). Test statistic =

H₀

There correlation between the ages of children and the number of vocabulary words they can say.

b. (5 points)

If there is a correlation between the ages of children and the number of vocabulary words they can say, then find the prediction equation and predict the number of vocabulary words a child can say if a child is 23 months old. Round answer to the nearest whole number. Include units. (Slope = 4.848, y-intercept = -56)

Prediction equation =

Prediction value =