It has become common, though potentially inaccurate, to believe that playing cla
ID: 3363124 • Letter: I
Question
It has become common, though potentially inaccurate, to believe that playing classical music to infants can increase their brain development, spatial awareness, and creativity. A child development specialist wants to test whether the exposure to Mozart’s calming compositions does in fact increase childhood neural development. He gathers a sample of 10 children chosen at random and tracks them from infancy through college. When each of his subjects turns 16, he administers an IQ test and then compares the results with the average hours a year the participant was played Mozart’s melodies as an infant.
IQ Score Hrs. of Mozart/Year
128 68
104 51
96 18
107 26
106 36
99 47
91 10
111 72
131 94
117 48
Calculate Pearson’s correlation coefficient and interpret the strength and direction of the results.
Using the correlation coefficient results, calculate the statistical significance of the relationship. Can the null hypothesis be rejected? In other words, does this relationship hold true for the population?
Explanation / Answer
to calculate pearsons correlation coefficient use excel . the excel path as follows :
menu -----> excel----->enter the data of IQ score ( y ) and data of Hours of Mozart / year (x ) in excel -----------> data -------->data analysis ------>regression ----->ok------> input Y range (select the data of IQ score ) ---------> input X range ( select the data of hours of mozart/ year )------> output range ( click on single blank box in excel )------>ok . the excel give the output as follows
the pearson correlation coefficient is denoted by r = 0.84 . the excel output is as follows :
SUMMARY OUTPUT Regression Statistics Multiple R 0.846114 R Square 0.715909 Adjusted R Square 0.680397 Standard Error 7.404703 Observations 10 ANOVA df SS MS F Significance F Regression 1 1105.363 1105.363 20.15996 0.002029 Residual 8 438.637 54.82963 Total 9 1544Related Questions
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