# AP Statistics Unit 7 Practice Test: Inference for Quantitative Data: Means

Test 7 for AP Stats.

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 Question 1

### When is it appropriate to use a one-sample t-interval for a mean?

 A When the population mean and standard deviation are both known. B When neither the population mean nor the standard deviation are known. C When the population mean is known but the population standard deviation is not. D When the population mean is unknown but the population standard deviation is known.
Question 1 Explanation:
When population standard deviation is not known, the appropriate confidence interval procedure for estimating the population mean of one quantitative variable for one sample is a one-sample t-interval for a mean. Answer C is correct.
 Question 2

### IV. As degrees of freedom increase, the area in the tails of a t-distribution decreases.

 A I and III B I and IV C II and III D II and IV
Question 2 Explanation:
A t-distribution differs from a normal distribution with more of the area allocated to the tails. The area in the tails decreases and degrees of freedom increase. Answer B is correct.
 Question 3

### 2.080

 A 0.5581 B 0.5597 C 0.5616 D 0.5762
Question 3 Explanation:
The formula is $t*(\dfrac{s}{\sqrt{n}})$ where $t*$ is the value obtained using degrees of freedom $(df=n-1)$ on a chart, s is the sample standard deviation, and n is the sample size. Answer C is correct.
 Question 4

### Which of the following statements is NOT true about the interpretation of a confidence interval?

 A We can be C% confident that the confidence interval for a population captures the population mean. B An interpretation of the confidence interval includes a reference to the sample and details about the population it represents. C Each interval is based on data from a random sample. D The confidence interval will be the same for every random sample.
Question 4 Explanation:
Because the data for every random sample will vary from sample to sample, the confidence interval will not be the same for every random sample. Answer D is correct.
 Question 5

### Which could be an appropriate null and alternative hypothesis for a one-sample t-test for a population mean?

 A $H_0:µ=µ_0 ,H_a:µ≠µ_0$ B $H_0:µ<µ_0 ,H_a:µ>µ_0$ C $H_0:µ≠µ_0 ,H_a:µ=µ_0$ D $H_0:µ=µ_0 ,H_a:µ≥µ_0$
Question 5 Explanation:
For a one-sample t-test, $H_0 is µ=µ_0$ where $µ_0$ is the hypothesized value. $H_a$ may be $µ<µ_0 , µ>µ_0$, or $µ≠µ_0$. Answer A is correct.
 Question 6

### What should an interpretation of the p-value of a significance test for a population mean recognize?

 A The p-value is computed by assuming the true population mean is equal to the value stated in the null hypothesis. B The p-value is computed by assuming the true population mean is equal to the value stated in the alternative hypothesis. C The p-value is computed by assuming the true population mean is not equal to the value stated in the null hypothesis. D The p-value is computed without input from the null or alternative hypothesis.
Question 6 Explanation:
The p-value is computed by assuming the true population mean is equal to the value stated in the null hypothesis. Because the alternative hypothesis is not a statement of equality, but of inequality, answer B is impossible. Answer A is correct.
 Question 7

### Which of the following is a necessary condition to calculate confidence intervals for the difference of two population means?

 A Sampling distribution of $(x_1-x_2)$ should be approximately normal; if skewed, either $n_1$ or $n_2$ must be greater than 30. B Sampling distribution of $(x_1-x_2)$ should be approximately normal; if skewed, both $n_1$ and $n_2$ must be greater than 30. C Sampling distribution of $(x_1-x_2)$ should be approximately normal; if skewed, $n_1$ and $n_2$ must be equal to 30. D None of the above are necessary conditions.
Question 7 Explanation:
To calculate confidence intervals for the difference of two population means, the sampling distribution should be approximately normal; if the observations are skewed, both $n_1$ and $n_2$ must be greater than 30. Answer B is correct.
 Question 8

### What effect does the sample size have on the width of a confidence interval for the difference of two means?

 A The width of the confidence interval for the difference of two means does not change as the sample sizes increase. B The width of the confidence interval for the difference of two means tends to increase as the sample sizes increase. C The width of the confidence interval for the difference of two means tends to increase exponentially as the sample sizes increase. D The width of the confidence interval for the difference of two means tends to decrease as the sample sizes increase.
Question 8 Explanation:
The width of the confidence interval for the difference of two means tends to decrease as the sample sizes increase, all other factors remaining the same. Answer D is correct.
 Question 9

### What could not be appropriate null and alternative hypotheses for a two-sample t-test for a difference of two population means?

 A $H_0:µ_1=µ_2 ,H_a:µ_1≤µ_2$ B $H_0:µ_1=µ_2 ,H_a:µ_1>µ_2$ C $H_0:µ_1-µ_2=0 ,H_a:µ_1<µ_2$ D $H_0:µ_1-µ_2=0 ,H_a:µ_1≠µ_2$
Question 9 Explanation:
An appropriate null hypothesis is a statement of inequality, either $µ_1=µ_2$ or $µ_1-µ_2=0$. An appropriate alternative hypothesis can not contain an overlapping statement, so $µ_1≤µ_2$ or $µ_1≥µ_2$ could not be appropriate alternative hypotheses. Answer A is correct.
 Question 10

### When conducting a test for the difference of two population means, what is the largest possible degree of freedom for sample sizes of 108 and 110.

 A 107 B 109 C 216 D 217
Question 10 Explanation:
The highest possible value for degrees of freedom is $n_1+n_2-2. 108+110-2=216$ so the highest possible degrees of freedom is 216. Answer C is correct.
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