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 95% confidence interval created from this data is (56.29, 65.09). This interval indicates:.Choose one or more:a. The average index of elementary school children must be 60.69.b. The standard deviation of the sample is about 10% smaller than the population standard deviation. c. That if we take many samples from this population 95% of them will have a sample mean between 56.29 and 65.09.d. 95% of all elementary school children in this district have indices between 56.29 and 65.09.e. 4.40 is 95% of the true average of the index for all elementary school children. f. We are 95% confident that the average index for all elementary school children is between 56.29 and 65.09.

Complete Question

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 95% confidence interval created from this data is (56.29, 65.09). This interval indicates:__________.Choose one or more:

a. The average index of elementary school children must be 60.69.

b. The standard deviation of the sample is about 10% smaller than the population standard deviation.

c. That if we take many samples from this population 95% of them will have a sample mean between 56.29 and 65.09.

d. 95% of all elementary school children in this district have indices between 56.29 and 65.09.

e. 4.40 is 95% of the true average of the index for all elementary school children.

f. We are 95% confident that the average index for all elementary school children is between 56.29 and 65.09.

The correct option is  a and  f

Step-by-step explanation:

From the question we are told that

    The sample size is  n =  16

     The 95% confidence interval is  (56.29, 65.09)

Generally the sample mean(average index of elementary school children) is mathematically represented as

=>  

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step-by-step explanation:

5050

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