Final answer:
Given the calculated t-statistic of 0.349 is less than the critical value of 2.045, we fail to reject the null hypothesis at the 0.05 significance level, which suggests no significant correlation between the variables in the regression model.
Step-by-step explanation:
To test H0: β=0 versus H1: β≠0 at the 0.05 significance level, we would typically use the t-test for the slope of the regression line.
For a simple linear regression model with the least squares estimate (LSE) of the slope as 0.3 and a standard error of 0.86 for the slope, we calculate the t-statistic by dividing the estimated slope by its standard error. This gives us a t-statistic of 0.3/0.86 ≈ 0.349.
Comparing this to the critical value of 2.045 for a two-tailed t-test with an α of 0.05 (assuming the degrees of freedom is correctly matched to the sample size, which in this case would typically be n-2), we see that 0.349 is less than 2.045.
Therefore, we fail to reject the null hypothesis, indicating that we do not have enough evidence to suggest that β is significantly different from 0. In other words, the study does not provide sufficient evidence for a significant correlation between the variables in the regression model.