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PLEASE ANSWER ALL of the questions correctly and please answer all the questions with what it regards in saying exactly, please and thank you take your time.

QUESTION 1-

While taking a course on mathematical biostatistics, your roommate recorded the number of hours they spent on a sample of ten assignment problems and the number of points each assignment was worth. Their data are shown below.

Number of hours spent (X): 1.7, 1.9, 1.8, 2.2, 0.4, 1.3, 2.8, 2.1, 1.4, 2.2 Number of points worth (Y): 8, 3, 8, 11, 2, 3, 12, 7, 7, 4

Test whether there is a significant (non-zero) correlation between the two variables.

a) Compute the sum of products and sums of squares for X and Y. Then use these quantities to compute the Pearson correlation coefficient.

b) Find the critical value for an alpha level of .05 and convert the Pearson correlation to a test statistic. Compare the observed test statistic with the critical value to decide whether the obtained correlation is significantly different from zero.

c) Dr. Purr had data from 31 cats on two variables, grooming (X) and fluffiness (Y). Unfortunately, she has lost the raw data, and all she has are the following summary statistics:

x = 18, Sy = 3, y = 51, Sy = 11,r = 0.3