A psychologist has designed an index to measure the social perceptiveness of elementary school children. The index is based on ratings of a child's responses to questions about a set of photographs showing different social situations. A random sample of 16 elementary school children was chosen, and their index measurements were recorded. Assume that the index measure in the population is normally distributed. The 90% confidence interval created from this data is (57.07, 64.31). This interval indicates:
Select one or more:
a. 3.62 is 90% of the true average of the index for all elementary school children.
b. The average index of elementary school children must be 60.69.
c. 90% of all elementary school children in this district have indices between 57.05 and 64.31.
d. If we take many samples from this population, 90% of them will have a sample mean between 57.05 and 64.31.
e. The standard deviation of the sample is about 10% smaller than the population standard deviation.
f. We are 90% confident that the average index for all elementary school children is between 57.05 and 64.31.