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

Test 9 for AP Stats.

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 Question 1

### What should be used to compute a confidence interval for the slope of a regression model?

 A A t-interval B A z-score C A p-value D A Chi-squared test
Question 1 Explanation:
The appropriate confidence interval for the slope of a regression model is a t-interval for the slope. Answer A is correct.
 Question 2

### Which of the following is not a condition to calculate confidence intervals for the slope of a regression model?

 A The relationship between x and y is linear. B The standard deviation for y varies with x. C Data is collected with a random sample. D The y-values are normally distributed or $n>30$.
Question 2 Explanation:
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.
 Question 3

### The slope of a given regression line of a sample size of 30 is 1.5, with a sample standard deviation s of 0.3 and a sample standard deviation of the x-values of 0.25. What is the margin of error for a critical value of 2.467?

 A 0.382 B 0.54 C 0.55 D 0.559
Question 3 Explanation:
The margin of error is t*SE, the standard error, which can be calculated by

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

$2.467*0.223≈0.550$

 Question 4

### 2.056

 A $0.386土2.074(0.082)$ B $0.386土2.064(0.082)$ C $0.386土2.056(0.082)$ D $0.082土2.074(0.386)$
Question 4 Explanation:
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.
 Question 5

### Which of the following describes the effects of sample size on the width of a confidence interval for the slope of a regression model?

 A As sample size increases, the width of the confidence interval increases. B As sample size increases, the width of the confidence interval decreases. C As sample size increases, the width of the confidence interval remains constant. D As sample size increases, the width of the confidence interval changes at random.
Question 5 Explanation:
All other factors remaining the same, the width of the confidence interval will decrease as the sample size increases. Answer B is correct.
 Question 6

### Which of the following would not be an appropriate null and alternative hypothesis for the slope of a regression model?

 A $H_0: β=β_0, H_a: β≠β_0$ B $H_0: β=β_0, H_a: β<β_0$ C $H_0: β=β0_, H_a: β>β_0$ D $H_0: β=β_0, H_a: β≤β_0$
Question 6 Explanation:
Appropriate alternative hypotheses can use <, >, or ≠ but cannot use ≤ or ≥ as this would overlap with the null hypothesis. Answer D is correct.
 Question 7

### Which of the following is a condition for the significance test for the slope of a regression model?

 A The true relationship between x and y is nonlinear. B The standard deviation for y does not vary with x. C For sampling without replacement, $n≤10%N$ D If the distribution of y-values is skewed, n should be at least 20.
Question 7 Explanation:
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.
 Question 8

### What is the distribution of the slope of a regression model, assuming all conditions are satisfied and the null hypothesis is true?

 A Normal distribution B Z-distribution C T-distribution D Chi-squared distribution
Question 8 Explanation:
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.
 Question 9

### How should one use the p-value to justify a claim based on the results of a significance test for the slope of a regression model?

 A If $p-value = a$, accept the null hypothesis. B If $p-value ≥ a$, reject the null hypothesis. C If $p-value ≤ a$, reject the null hypothesis. D If $p-value ≠ a$, accept the null hypothesis.
Question 9 Explanation:
If the $p-value ≤ a$, then reject the null hypothesis; if $p-value>a$, accept the null hypothesis. Answer C is correct.
 Question 10

### A student took a random sample of other students and found a linear relationship between the number of minutes spent in the library and ACT scores. A 95% confidence level for the slope of the regression line was (15, 55). The student wants to use this interval to test $H_0: β=β_0, H_a: β≠β_0$ at the α=0.05 level of significance. What is an appropriate conclusion?

 A Fail to reject $H_0$, and fail to conclude a linear relationship between library use and ACT scores. B Fail to reject $H_0$, suggesting a linear relationship between library use and ACT scores. C Reject $H_0$, and fail to conclude a linear relationship between library use and ACT scores. D Reject $H_0$, suggesting a linear relationship between library use and ACT scores.
Question 10 Explanation:
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.
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