3 years ago

Which of the following statements is the only sentence that is error-free?

Mathematics

1 answer:

Ray Of Light [21]3 years ago

5 0

I don’t really know what the answer is

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As the carbon content in steel increases, its ductility tends to decrease. A researcher at a steel company measures carbon conte

mixer [17]

Answer:

d. -5.666 to -0.926

Step-by-step explanation:

Here a pivotal quantity is $T = \frac{\hat{\beta_{1}}-\beta_{1}}{se(\hat{\beta_{1}})}$ where $\beta_{1}$ is the true slope of the regression equation (unknown), $\hat{\beta_{1}}$ is its least square estimate and $se(\hat{\beta_{1}})=1.097$ is its estimated standard error. And T has t-distribution with n-2=15-2=13 degrees of freedom (n is the sample size). We have that $\hat{\beta_{1}} = -3.30$ , and because we want the 95% confidence interval, we should use the 2.5th quantile of the t distribution with 13 df, this value is -2.16 and the 95% confidence intervale is given by $\hat{\beta_{1}}\pm t_{0.025}se(\hat{\beta_{1}})$ , i.e., $-3.30\pm (2.16)(1.097)$ . Therefore, the 95% confidence interval explicitly is (-5.666, -0.926)