Test 7 for AP Stats.
Congratulations - you have completed .
You scored %%SCORE%% out of %%TOTAL%%.
Your performance has been rated as %%RATING%%
Your answers are highlighted below.
Question 1 |
When is it appropriate to use a one-sample t-interval for a mean?
When the population mean and standard deviation are both known. | |
When neither the population mean nor the standard deviation are known. | |
When the population mean is known but the population standard deviation is not. | |
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 |
Which statements are true of t-distributions?
I. More of the area of the distribution is allocated to the tails than in a normal distribution.
II. Less of the area of the distribution is allocated to the tails than in a normal distribution.
III. As degrees of freedom increase, the area in the tails of a t-distribution increases.
IV. As degrees of freedom increase, the area in the tails of a t-distribution decreases.
I and III | |
I and IV | |
II and III | |
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 |
What is the margin of error for a one-sample t-interval with sample size 20 and sample standard deviation 1.2 with a confidence level of 95%? Use the condensed table of values below.
df |
95% |
19 |
2.093 |
20 |
2.086 |
21 |
2.080 |
0.5581 | |
0.5597 | |
0.5616 | |
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?
We can be C% confident that the confidence interval for a population captures the population mean. | |
An interpretation of the confidence interval includes a reference to the sample and details about the population it represents. | |
Each interval is based on data from a random sample. | |
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?
$H_0:µ=µ_0 ,H_a:µ≠µ_0$ | |
$H_0:µ<µ_0 ,H_a:µ>µ_0$ | |
$H_0:µ≠µ_0 ,H_a:µ=µ_0$ | |
$H_0:µ=µ_0 ,H_a:µ≥µ_0$ |
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?
The p-value is computed by assuming the true population mean is equal to the value stated in the null hypothesis. | |
The p-value is computed by assuming the true population mean is equal to the value stated in the alternative hypothesis. | |
The p-value is computed by assuming the true population mean is not equal to the value stated in the null hypothesis. | |
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?
Sampling distribution of $(x_1-x_2)$ should be approximately normal; if skewed, either $n_1$ or $n_2$ must be greater than 30. | |
Sampling distribution of $(x_1-x_2)$ should be approximately normal; if skewed, both $n_1$ and $n_2$ must be greater than 30. | |
Sampling distribution of $(x_1-x_2)$ should be approximately normal; if skewed, $n_1$ and $n_2$ must be equal to 30. | |
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?
The width of the confidence interval for the difference of two means does not change as the sample sizes increase. | |
The width of the confidence interval for the difference of two means tends to increase as the sample sizes increase. | |
The width of the confidence interval for the difference of two means tends to increase exponentially as the sample sizes increase. | |
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?
$H_0:µ_1=µ_2 ,H_a:µ_1≤µ_2$ | |
$H_0:µ_1=µ_2 ,H_a:µ_1>µ_2$ | |
$H_0:µ_1-µ_2=0 ,H_a:µ_1<µ_2$ | |
$H_0:µ_1-µ_2=0 ,H_a:µ_1≠µ_2$ |
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.
107 | |
109 | |
216 | |
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.
Once you are finished, click the button below. Any items you have not completed will be marked incorrect.
There are 10 questions to complete.
|
List |