Statistical Inference about Slope: Answers | Saylor Academy | Saylor Academy

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This section further details two types of inferences on the slope parameter, considering both confidence intervals and hypothesis testing.

Answers

1.

$0.743±0.578$

3.

$−0.610±0.633$

5.

$T=1.732$ ,

$±t_{0.05}=±2.353$ , do not reject

$H_0$

7.

$0.6±0.451$

9.

$T=−4.481$ ,

$±t_{0.005}=±3.355$ , reject

$H_0$

11.

$4.8±1.7 words$

13.

$T=2.843$ ,

$±t_{0.05}=±1.860$ , reject

$H_0$

15.

$42.024±28.011$ thousand dollars,
$T=1.487$ , $t_{0.05}=1.943$ , do not reject $H_0$ ;
$t_{0.10}=1.440$ , reject $H_0$

17.

$T=4.096$ ,

$±t_{0.05}=±1.771$ , reject

$H_0$

19.

$T=25.524$ ,

$±t_{0.0005}=±3.505$ , reject

$H_0$

21.

$2.550±0.127$ hundred psi,
$T=41.072$ , $±t_{0.005}=±3.674$ , reject $H_0$

23.

$(0.0014,0.0018)$
$H_0: β_1=0.001$ vs. $H_a: β_1 > 0.001$ . Test Statistic: $Z=6.1625$ . Rejection Region: $[1.28,+∞)$ .

Decision: Reject $H_0$ .

25.

$(101.789,131.4435)$
$H_0: β_1=90$ vs. $H_a: β_1 > 90$ . Test Statistic: $T=3.5938$ . $d.f.=58$ . Rejection Region: $[1.296,+∞)$ .

Decision: Reject $H_0$ .