Question

Using R output provided

> summary(ls) Call: Residuals: Min 1Q Median 3Q Max 0.20283 -0.14691 -0.02255 0.06655 0.44541 Coefficients: (Intercept) 0.365100.099043.686 0.003586 ** Signif. codes: 0 '***' 0.001 '0.01 '*'0.05 '.' 0.1''1 Estimate Std. Error t value Pr>Itl) 0.96683 0.18292 5.286 0.000258** Residual standard error: 0.1932 on 11 degrees of freedom Multiple R-squared 0.7175, Adjusted R-squared: 0.6918 F-statistic: 27.94 on 1 and 11 DF, p-value: 0.0002581 anovaCLs) Analysis of Variance Table Response: y Df Sum Sq Mean Sq F value POF) 1 1.04275 1.04275 27.937 0.0002581 Residuals 11 0.41057 0.03732 Signif. codes: 0 ***' 0.001 '*0.01 *'0.05 '.' 0.1 '' 1

1). Perform hypothesis testing for B(beta)1=2 using A(alpha)=0.05

Answer 1

$H_0: \beta_1 = 2$

$H_1: \beta_1 \neq 2$

$t_0 = \frac{\hat \beta_1 - \beta_1}{se(\hat \beta_1)} = \frac{0.96683 - 2}{0.18292} = -5.648$

Critical value,

$t_{0.025, 11} = 2.201$

Now, $|t_0| > 2.201$

So we reject the null hypothesis and conclude with 95% confidence that $\beta_1$ value is not equal to 2.

** If this answer does not match please comment.