Question

Glassblowers often price their pieces based on the number of hours spent making them. Given below is a table showing x = #hours and y = price. x: 26, 27, 33, 29, 29, 34, 30, 40, 22 y: 540, 555, 575, 577, 606, 661, 738, 804, 496 The linear correlation coefficient for this data is r = .829 We want to test, at level q = .05 the claim that the populations of hours and prices are positively linearly correlated. a) What is the parameter we want to test? b) State the Null and Alternate Hypotheses. c) Find the Rejection Rejection and Compute the Test Stat d) What is the conclusion of your test?

Answer 1

SOLUTION-

LET BE THE POPULATION CORRELATION COEFFICIENT BETWEEN THE VARIABLES.

1.) THE NULL AND THE ALTERNATE HYPOTHESIS FRAMED IS AS:

2.) THE TEST STATISTIC IS DEFINED AS,

HERE, r=0.829 and n=9

HENCE,

WE REJECT THE NULL HYPOTHESIS IF P-VALUE< 0.05.

THE P-VALUE FOR THE T-VALUE IS 0.006, WHICH IS <0.05. HENCE, WE REJECT THE NULL HYPOTHESIS.

3.) HENCE, WE CAN CONCLUDE THAT THERE IS A STRONG LINEAR ASSOCIATION BETWEEN THE VARIABLES.

****IN CASE OF DOUBT, COMMENT BELOW. ALSO LIKE THE SOLUTION, IF POSSIBLE.