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Think and Answer requires you to answer two questions

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Think and Answer requires you to answer two questions. For each question, do not simply provide an answer; make sure you explain how you arrived at that answer. Even if your reasoning is wrong, you will still be credited for participation.

Answer the following question:

1. Why cannot a confidence level be 100%?

2. Why is it recommended to formulate a hypothesis so that it becomes the alternative (but not null) hypothesis?

True or False?

3. The higher the confidence level, the narrower the confidence interval.

4. If we fail to reject the null hypothesis, we reject the alternative hypothesis.

HW 4

Ch. 7

Sec. 7-1:

 

1. Poll Results in the Media USA Today provided results from a poll of 1000 adults who were asked to identify their favorite pie. Among the 1000 respondents, 14% chose chocolate pie, and the margin of error was given as ± 4 percentage points. What important feature of the poll was omitted?
    
2. Margin of Error For the poll described in Exercise 1, describe what is meant by the statement that “the margin of error was given as ± 4 percentage points.”

 

Finding Critical Values. In Exercises 5–8, find the critical value zα/2 that corresponds to the given confidence level.

5. 90%

    6.    99%

 

Formats of Confidence Intervals. In Exercises 9–12, express the confidence interval using the indicated format. (The confidence intervals are based on the proportions of red, orange, yellow, and blue M&Ms in Data Set 27 “M&M Weights” in Appendix B.)

Formats of Confidence Intervals. In Exercises 9–12, express the confidence interval using the indicated format. (The confidence intervals are based on the proportions of red, orange, yellow, and blue M&Ms in Data Set 27 “M&M Weights” in Appendix B.)

9. Red M&Ms Express 0.0434 < p < 0.217 in the form of p^± E.

 

 Constructing and Interpreting Confidence Intervals. In Exercises 13–16, use the given sample data and confidence level. In each case, (a) find the best point estimate of the population proportion p; (b) identify the value of the margin of error E; (c) construct the confidence interval; (d) write a statement that correctly interprets the confidence interval.

13. Mickey D’s In a study of the accuracy of fast food drive-through orders, McDonald’s had 33 orders that were not accurate among 362 orders observed (based on data from QSR magazine). Construct a 95% confidence interval for the proportion of orders that are not accurate.

 

16. Medical Malpractice In a study of 1228 randomly selected medical malpractice lawsuits, it was found that 856 of them were dropped or dismissed (based on data from the Physicians Insurers Association of America). Construct a 95% confidence interval for the proportion of medical malpractice lawsuits that are dropped or dismissed.
 

19.

Fast Food Accuracy In a study of the accuracy of fast food drive-through orders, Burger King had 264 accurate orders and 54 that were not accurate (based on data from QSR magazine).

1. Construct a 99% confidence interval estimate of the percentage of orders that are not accurate.
2. Compare the result from part (a) to this 99% confidence interval for the percentage of orders that are not accurate at Wendy’s: 6.2% < p < 15.9%. What do you conclude?,

Determining Sample Size. In Exercises 31–38, use the given data to find the minimum sample size required to estimate a population proportion or percentage.

31. Lefties Find the sample size needed to estimate the percentage of California residents who are left-handed. Use a margin of error of three percentage points, and use a confidence level of 99%.
    1. Assume that p^and q^are unknown.
    2. Assume that based on prior studies, about 10% of Californians are left-handed.
    3. How do the results from parts (a) and (b) change if the entire United States is used instead of California?
32. Chickenpox You plan to conduct a survey to estimate the percentage of adults who have had chickenpox. Find the number of people who must be surveyed if you want to be 90% confident that the sample percentage is within two percentage points of the true percentage for the population of all adults.
    4. Assume that nothing is known about the prevalence of chickenpox.
    5. Assume that about 95% of adults have had chickenpox.
    6. Does the added knowledge in part (b) have much of an effect on the sample size?

 

Sec. 7-2:

 

Statistical Literacy and Critical Thinking

In Exercises 1–3, refer to the accompanying screen display that results from the Verizon airport data speeds (Mbps) from Data Set 32 “Airport Data Speeds” in Appendix B. The confidence level of 95% was used.

TI-83/84 Plus

 

 

 

1. Airport Data Speeds Refer to the accompanying screen display.
   • Express the confidence interval in the format that uses the “less than” symbol. Given that the original listed data use one decimal place, round the confidence interval limits accordingly.
   • Identify the best point estimate of μ and the margin of error.
   • In constructing the confidence interval estimate of μ, why is it not necessary to confirm that the sample data appear to be from a population with a normal distribution?
2. Degrees of Freedom
   • What is the number of degrees of freedom that should be used for finding the critical value tα/2?
   • Find the critical value tα/2 corresponding to a 95% confidence level.
   • Give a brief general description of the number of degrees of freedom.

 

 

Confidence Intervals. In Exercises 9–24, construct the confidence interval estimate of the mean.

9. Birth Weights of Girls Use these summary statistics given in Exercise 8: n = 205,x= 30.4 hg, s = 7.1 hg. Use a 95% confidence level. Are the results very different from those found in Example 2 with only 15 sample values?

 

12. Atkins Weight Loss Program In a test of weight loss programs, 40 adults used the Atkins weight loss program. After 12 months, their mean weight loss was found to be 2.1 lb, with a standard deviation of 4.8 lb. Construct a 90% confidence interval estimate of the mean weight loss for all such subjects. Does the Atkins program appear to be effective? Does it appear to be practical?

 

14. Garlic for Reducing Cholesterol In a test of the effectiveness of garlic for lowering cholesterol, 49 subjects were treated with raw garlic. Cholesterol levels were measured before and after the treatment. The changes (before minus after) in their levels of LDL cholesterol (in mg/dL) had a mean of 0.4 and a standard deviation of 21.0 (based on data from “Effect of Raw Garlic vs Commercial Garlic Supplements on Plasma Lipid Concentrations in Adults with Moderate Hypercholesterolemia,” by Gardner et al., Archives of Internal Medicine, Vol. 167). Construct a 98% confidence interval estimate of the mean net change in LDL cholesterol after the garlic treatment. What does the confidence interval suggest about the effectiveness of garlic in reducing LDL cholesterol?

23.Student Evaluations Listed below are student evaluation ratings of courses, where a rating of 5 is for “excellent.” The ratings were obtained at the University of Texas at Austin. (See Data Set 17 “Course Evaluations” in Appendix B.) Use a 90% confidence level. What does the confidence interval tell us about the population of college students in Texas?

3.8, 3.0, 4.0, 4.8, 3.0, 4.2, 3.5, 4.7, 4.4, 4.2, 4.3, 3.8, 3.3, 4.0, 3.8

 

Ch. 8

Sec. 8-1:

1. Vitamin C and Aspirin A bottle contains a label stating that it contains Spring Valley pills with 500 mg of vitamin C, and another bottle contains a label stating that it contains Bayer pills with 325 mg of aspirin. When testing claims about the mean contents of the pills, which would have more serious implications: rejection of the Spring Valley vitamin C claim or rejection of the Bayer aspirin claim? Is it wise to use the same significance level for hypothesis tests about the mean amount of vitamin C and the mean amount of aspirin?

 

Identifying H0 and H1. In Exercises 5–8, do the following:

• Express the original claim in symbolic form.
• Identify the null and alternative hypotheses.

5. Online Data Claim: Most adults would erase all of their personal information online if they could. A GFI Software survey of 565 randomly selected adults showed that 59% of them would erase all of their personal information online if they could.
    
6. Cell Phone Claim: Fewer than 95% of adults have a cell phone. In a Marist poll of 1128 adults, 87% said that they have a cell phone.

 

Test Statistics. In Exercises 13–16, refer to the exercise identified and find the value of the test statistic. (Refer to Table 8-2 on page 362 to select the correct expression for evaluating the test statistic.)

13. Exercise 5 “Online Data”
     
14. Exercise 6 “Cell Phone”

 

 

Final Conclusions. In Exercises 25–28, use a significance level of α = 0.05 and use the given information for the following:

1. State a conclusion about the null hypothesis. (Reject H0 or fail to reject H0)
2. Without using technical terms or symbols, state a final conclusion that addresses the original claim.

25. Original claim: More than 58% of adults would erase all of their personal information online if they could. The hypothesis test results in a P-value of .3257.
     
26. Original claim: Fewer than 90% of adults have a cell phone. The hypothesis test results in a P-value of 0.0003.