AP Statistics Unit 9 Practice Test: Inference for Quantitative Data: Slopes

The appropriate confidence interval for the slope of a regression model is a t-interval for the slope. Answer A is correct.

The following conditions must be checked to calculate confidence intervals for the slope of a regression line: the true relationship between x and y is linear, the standard deviation for y does not vary with x (all x should have approximately equal standard deviations), data should be collected with a random sample or randomized experiment and if data is collected without replacement then $n≤10%n$, and the y-values are normally distributed (if the distribution is skewed, n should be greater than 30). Answer B is not a condition.

The margin of error is t*SE, the standard error, which can be calculated by

$ \dfrac{s}{s_x\sqrt{n-1}} = \dfrac{0.3}{0.25\sqrt{29}} ≈ 0.223$

$2.467*0.223≈0.550$

Answer C is correct.

The interval estimate is $b土t*(SE_b)$. In this case, $b=0.386, SE_b=0.082$, and $t* = 2.074 (p=0.025$ with $df n-2=24-2=22)$. The correct set-up for the calculation is $0.386土2.074(0.082)$ and answer A is correct.

All other factors remaining the same, the width of the confidence interval will decrease as the sample size increases. Answer B is correct.

Appropriate alternative hypotheses can use <, >, or ≠ but cannot use ≤ or ≥ as this would overlap with the null hypothesis. Answer D is correct.

Conditions for the significant test include that the true relationship between x and y is nonlinear, the standard deviation for y does not vary with x, $n≤10%N$ for sampling without replacement, and $n>30$ if the distribution of y-values is skewed. Answer C is correct.

The distribution of the slope of a regression model, assuming all conditions are satisfied and the null hypothesis is true, is a t-distribution. Answer C is correct.

If the $p-value ≤ a$, then reject the null hypothesis; if $p-value>a$, accept the null hypothesis. Answer C is correct.

The null hypothesis says there is no relationship, that the slope of the regression line = 0. Because the confidence interval does not contain zero, the student can reject the null hypothesis and conclude that there is a linear relationship between library use and ACT scores. Answer D is correct.