Question

Use the following data and conduct a two-tailed hypothesis test using a = .05. a. What are EX, EY, (EX)(EY)? b. What is 2.XY? c. What are your hypotheses? d. What are your degrees of freedom? e. What is the critical value? f. What is the value of Pearson r? g. What do you conclude?

Answer 1

Χ Τ Υ Ι Υ.Υ Χ.Υ 54 112 36 Χ. Χ 81 256 576 144 49 324 ΣΧ= 84, ΣΥ= 38 ΣΧ.ΣΥ = 84-38 =3192 ΣΧ.Υ = 620, ΣΧ2 = 1406, ΣΥ? = 278 The null and alternvative hypothesis is, H, :ρ= 0 H, :ρά 0 The degree of freedom is, df = n-2 = 6-2 = 4 Critical value:

The corresponding critical correlation value re for a significance level of a = 0.05, for a two-tailed test is: r = 0.95 The correlation coefficient is, n. XY-EX Y V[r{X? - (EX)*] . [n Y? - (EY)?] 6.620 - 84.38 0.9497 V[6.1406 – 842] • [6.278 – 38? The rejection region is, , the null hypothesis is rejected if r>re = 0.95 Since the test statistic is less than critical value, so we fail to reject the null hypothesis Conclusion: it can be conclude that there is no correlation exists between the variables