1. Inference About Variables Part IV Review
BPS 7e Chapter 24
© 2015 W. H. Freeman and Company

2. Central Limit Theorem The Central Limit Theorem:
suggests why the Normal distributions are common models for observed data.
allows us to use Normal probability calculations to answer questions about sample means from many observations, even when the population distribution is not Normal.
suggests that, when the sample is large enough, the distribution of x̄ is very close to Normal.
All of the above

3. Central Limit Theorem (answer)
The Central Limit Theorem:
suggests why the Normal distributions are common models for observed data.
allows us to use Normal probability calculations to answer questions about sample means from many observations, even when the population distribution is not Normal.
suggests that, when the sample is large enough, the distribution of x̄ is very close to Normal.
All of the above

4. Sample Proportions
The proportion p of California drivers without insurance is a parameter describing the population of California drivers. To estimate p, we take a simple random sample (SRS) of 300 California drivers and find that 45 do not have insurance. The sample proportion p^ (p-hat) of these subjects without insurance is:
0.18.
0.175.
0.15.
0.225.

5. Sample Proportions (answer)
The proportion p of California drivers without insurance is a parameter describing the population of California drivers. To estimate p, we take a simple random sample (SRS) of 300 California drivers and find that 45 do not have insurance. The sample proportion p^ (p-hat) of these subjects without insurance is:
0.18.
0.175.
0.15.
0.225.

6. Reasoning of Estimation
In repeated sampling, x̅ should be within ______ of  95% of the time.
2 s
+/– 2 s / s
+/– s /

7. Reasoning of Estimation (answer)
In repeated sampling, x̅ should be within ______ of  95% of the time.
2 s
+/– 2 s / s
+/– s /

8. One-Sample t Confidence Interval
Nine randomly sampled students were asked how many hours of TV they watched last week. x̅ was 3.5 h and s was 4 h. For 95% confidence and 8 degrees of freedom, t* = 2.3. The stemplot was somewhat skewed to the right, with no outliers. What is the 95% confidence interval for m?
3.5 ± (2.3 × 3)
3.5 ± (2.3 × 4/9)
3.5 ± (2.3 × 4 × 9)
3.5 ± (2.3 × 4/3)
should not be calculated

9. One-Sample t Confidence Interval (answer)
Nine randomly sampled students were asked how many hours of TV they watched last week. x̅ was 3.5 h and s was 4 h. For 95% confidence and 8 degrees of freedom, t* = 2.3. The stemplot was somewhat skewed to the right, with no outliers. What is the 95% confidence interval for m?
3.5 ± (2.3 × 3)
3.5 ± (2.3 × 4/9)
3.5 ± (2.3 × 4 × 9)
3.5 ± (2.3 × 4/3)
should not be calculated

10. Choosing the Sample Size
If we are to decrease the acceptable margin of error from 0.05 to 0.03, the required sample size will:
Decrease.
remain the same.
Increase.

11. Choosing the Sample Size (answer)
If we are to decrease the acceptable margin of error from 0.05 to 0.03, the required sample size will:
Decrease.
remain the same.
Increase.

12. Two-Sample t Procedures
A dairy scientist compared milk production of cows fed two different diets. He randomly divided a set of 20 cows into two groups. One group was fed diet 1 for a month, and the other was fed diet 2 for a month. Here are the milk production results (lb/week):
What is the standard error of x̅1 ─ x̅2?
group n x̅ s
diet 1 20
385.7
25.7
diet 2
398.2
43.1

13. Two-Sample t Procedures (answer)
A dairy scientist compared milk production of cows fed two different diets. He randomly divided a set of 20 cows into two groups. One group was fed diet 1 for a month, and the other was fed diet 2 for a month. Here are the milk production results (lb/week):
What is the standard error of x̅1 ─ x̅2?
group n x̅ s
diet 1 20
385.7
25.7
diet 2
398.2
43.1

14. The Sample Proportion
The sampling distribution of p̂ gives the _____ of possible values of p̂ along with _______ of those values for simple random samples of the same ____ from the same population.
size; probabilities; range
range; probabilities; size
probabilities; range; size
size; range; probabilities

15. The Sample Proportion (answer)
The sampling distribution of p̂ gives the _____ of possible values of p̂ along with _______ of those values for simple random samples of the same ____ from the same population.
size; probabilities; range
range; probabilities; size
probabilities; range; size
size; range; probabilities

16. Comparing Two Means
Researchers want to examine if males and females differ in their reactions to a new drug called X. For the experiment, a fixed dose will be given to 20 randomly selected males and 20 randomly selected females. Periodic measurements will be made to determine the time it takes until a desired level of drug is present in the blood for each subject. The researchers want to determine whether there is a gender difference in the average speed at which the drug is absorbed into the blood system.
To compare the means, they should test the hypotheses ___________ and ____________.
H0: m males = m females; Ha: m males ≠ m females
H0: x̅ males = x ̅ females; Ha: x ̅ males < x̅ females
H0: m males ≠ m females ; Ha: m males = m females
H0: x̅ males ≠ x̅ females ; Ha: x ̅ males = x̅ females

17. Comparing Two Means (answer)
Researchers want to examine if males and females differ in their reactions to a new drug called X. For the experiment, a fixed dose will be given to 20 randomly selected males and 20 randomly selected females. Periodic measurements will be made to determine the time it takes until a desired level of drug is present in the blood for each subject. The researchers want to determine whether there is a gender difference in the average speed at which the drug is absorbed into the blood system.
To compare the means, they should test the hypotheses ___________ and ____________.
H0: m males = m females; Ha: m males ≠ m females
H0: x̅ males = x ̅ females; Ha: x ̅ males < x̅ females
H0: m males ≠ m females ; Ha: m males = m females
H0: x̅ males ≠ x̅ females ; Ha: x ̅ males = x̅ females

18. Conditions for Inference
True or False: Any inference procedure based on sample statistics like the sample mean x̅ that are not resistant to outliers can be strongly influenced by a few extreme observations.
True
False

19. Conditions for Inference (answer)
True or False: Any inference procedure based on sample statistics like the sample mean x̅ that are not resistant to outliers can be strongly influenced by a few extreme observations.
True
False

20. Cautions About Significance Tests
Researchers wanted to know if there was a difference in math achievement scores in school X from year 2006 to The average math score in 2006 was 315. In 2007, the score increased to 326. The difference provided a P-value of Were these results statistically significant?
no, because an 11-point difference is probably too small to really matter
no, because the P-value is small
yes, because the P-value is small
yes, because the difference of 11 points is bigger than 0

21. Cautions About Significance Tests (answer)
Researchers wanted to know if there was a difference in math achievement scores in school X from year 2006 to The average math score in 2006 was 315. In 2007, the score increased to 326. The difference provided a P-value of Were these results statistically significant?
no, because an 11-point difference is probably too small to really matter
no, because the P-value is small
yes, because the P-value is small
yes, because the difference of 11 points is bigger than 0

22. Two Proportions
We want to test whether proportions from two populations are different from each other. What are the appropriate null and alternative hypotheses?
H0: p1 = p2, Ha: p1 ≠ p2
H0: p1 ≠ p2, Ha: p1 = p2
H0: p1 = p2, Ha : p1 > p2
H0: p̂1 = p̂2, Ha: p̂1 ≠ p̂2
H0: p̂1 = p̂2, Ha : p̂1 ≠ p̂2

23. Two Proportions (answer)
We want to test whether proportions from two populations are different from each other. What are the appropriate null and alternative hypotheses?
H0: p1 = p2, Ha: p1 ≠ p2
H0: p1 ≠ p2, Ha: p1 = p2
H0 : p1 = p2, Ha: p1 > p2
H0: p̂1 = p̂2, Ha: p̂1 ≠ p̂2

24. Cautions About Significance Tests
A company is working on a brand new car model with a radical new design. If tests are successful, the company will invest millions of production and marketing dollars. Which value of a should they use in their test?
0.10
0.05
0.01
None of the above

25. Cautions About Significance Tests (answer)
A company is working on a brand new car model with a radical new design. If tests are successful, the company will invest millions of production and marketing dollars. Which value of a should they use in their test?
0.10
0.05
0.01
None of the above