A psychologist has designed an index to measure the social perspectives 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. The following are the indices measured on a random sample of 16 children attending elementary school in a particular district.

48, 75, 69, 58, 60, 68, 59, 66, 71, 52, 49, 60, 54, 55, 70, 57

For the data, the mean index is 60.69 and the standard deviation is 8.26.

Perform a statistical test to determine if the population mean index is greater than 50.

H₀:

H_A:

a). Test Statistic =

b). P-value =

c). Rejection region=

d).Decision in the context of the problem=