The article “A Study of Factors Affecting the Human Cone Photoreceptor Density Measured by Adaptive Optics Scanning Laser Ophthalmoscope” included a summary of a multiple regression analysis. The analysis used a sample of 192 eyes to examine the relationship between cone cell packing density and two independent variables: eccentricity and axial length. The estimated standard error of the coefficient on axial length was 134.350. Test the null hypothesis H0: β2=0 against the alternative Ha: β2≠0 using a significance level of .05, and interpret the result.
To test the null hypothesis H0: β2=0 against the alternative Ha: β2≠0, we calculate the test statistic using the estimated coefficient on axial length (-348.037) and the standard error (134.350). The test statistic is -2.59. Since this is a two-tailed test, we calculate the corresponding P-value for df=189 and α/2=0.025. The P-value is approximately 0.01. Since the P-value is less than the significance level of 0.05, we reject the null hypothesis. This provides sufficient evidence to conclude that the alternative hypothesis is true.