Question

In the table below, 4 students' GPA and hours spent on sleep. 3. Hours on Sleep Student ID GPA 4 4 10 3 3 6. 3 4 4 1) Calculate the correlation coefficient. 2) Based on the correlation coefficient, the relationship between GPA and sleep is negative. True/ FALSE. 2 points 3) With alpha = 0.05, can you reject the null hypothesis that there is no relationship between GPA and hours spent on sleep.

Answer 1

Answer Date: 19/12/2019 The data represent GPA (x) and hours spent on sleep (v). The correlation coefficient is, First, compute the calculation table then find correlation coefficient. The calculation table is, X 4 | Y 8 | X2 16 XY 32 4 10 16 40 Y2 64 100 36 16 216 4 28 9 9 50 18 12 102 Total 14 | The correlation coefficient is,

1 = - ηΣυν- (ΣΙΣ») Σ?)-(Σ & Σy?)-(Σ» 4x102 – 14x 28 4 x 50 - (14) 4 x 216- (28) = 0.8944 The correlation coefficientis (0.8944). 2) Based on correlation coefficient, the relationship between GPA and sleep is negative. The statement is False. Due to the relationship between GPA and sleep is positive.

To test the hypothesis is that there is a relationship between GPA and hours spent on sleep at 5% significance level. The null and alternative hypothesis is, H :p=0 H:860 The t-test statistics is, rx √n-2 t=- V1-r2 0.8944 x 14-2 1-(0.8944)2 = 2.828 The t-test statistics is 2.828. The t-critical value is,

The sample size is small and two-tailed test. Look in the column headed a= 0.05 and the row headed in the t distribution table by using degree of freedom is, d.f.=n-2 = 4-2 = 2 The t-critical value is – 4.303 and 4.303| Decision The statistical decision is that the t-test statistics which is 2.828 is less than t-critical value which is 4.303, so the null hypothesis is not rejected. There is insufficient evidence to indicate that there is a relationship between GPA and hours spent on sleep. The result is not statistically significant.