1. Find the critical value, Z_/2, that corresponds to a confidence level of 93.14% Z_/2=

2. Assume that a random sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the given values and confidence level: n = 90, x = 27, with a(n) 89.4% level of confidence. E =

3. Assume that a random sample is used to estimate a population proportion p. Construct the confidence interval about the population proportion that corresponds to the given values and confidence level: n = 140, x = 56, with a(n) 78% level of confidence.

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4. A survey of 70 randomly selected adults was conducted to determine if they thought there should be a ban on high capacity ammunition magazines. Out of the 70 people surveyed, 28 people thought there should be a ban on high capacity ammunition magazines. Determine the interval estimate of population proportion, p, with a confidence level of 84%.

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5. A survey of 50 randomly selected adults asked the question "Are genetically modified foods bad for humans to consume?" Out of the 50 people surveyed, 30 people incorrectly answered "yes". Determine the interval estimate of population proportion of those people that incorrectly answered "yes" to the question "Are genetically modified foods bad for humans to consume?", with a confidence level of 85%.

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6. A survey of randomly selected students at Texas Tech University wished to determine the proportion of students who would correctly answer the question "Who won the U.S. Civil War?" A previous survey at the same university had determined that 21% had answered the question correctly. At the 98% level of confidence, determine the minimum sample size necessary to estimate the interval estimate, within 2.5% of population proportion, of those the students at Texas Tech that would answer the question correctly.

7. An opinion poll was to be conducted in order to determine how well a particular congressional incumbent was doing at his job. This was the first poll to be conducted on this incumbent, so, the pollsters had no record to go on for past performance. The question to be asked is "Do you approve of the job Congressperson Smith is doing while in office?" The answer is a simple "yes" or "no." At the 90% level of confidence, what minimum sample size is necessary to be to sure that the poll is within 3% of the population proportion of those that would answer "yes" to this question?

8. A random sample of 32 FSA actuaries' annual incomes was collected and the mean income was calculated to be $159000. It is known that the population standard deviation for this data is $9540. At the 95% level of confidence, construct the confidence interval about the population mean for this data.

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9. As part of an effort to improve their customers' experience, a bank needs to determine the current average wait time for a customer to see a teller. This information will be used to try to incorporate a new system to cut wait times. A study of 75 randomly selected customers determined that the mean wait time was 144 seconds with a standard deviation of 14.4 seconds. At the 95% level of confidence, construct the confidence interval about the population mean for this data.

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10. An auditor conducted a study to determine how many minutes a particular doctor spends with each of his patients for an office visit. He observed several patients and the amount of time the doctor spent with each; the collected data is shown below as minutes spent per patient. With a 0.01 level of significance, construct the confidence interval about the population mean for the number of minutes spent with each patient by this particular doctor.

{10.25, 7, 13.75, 19, 14, 7.75, 6.5, 9.5, 10.25, 13.5}

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11. A survey of the price of gewgaws determined that when a random sample of 62 gewgaws had been collected, the price varied from $188 to $263.2 and the mean price was $223.7. With a 0.01 level of significance, construct the confidence interval about the population mean for the price of the gewgaws.

Type your answer in the form (lowerValue, upperValue)

12. A medical researcher wants to conduct a study on the birth weight of babies born to mothers who smoked throughout their pregnancy. If she wishes to be within 46 grams, at the 0.1 level of significance, Determine the minimum sample size necessary for this study. A pilot study by this researcher found standard deviation to be 446.8 grams.

13. Dowsing is the action of a person--called the dowser--using a rod, stick, or object hung from a string--called a dowsing rod, dowsing stick, doodlebug (when used to locate oil), divining rod, or pendulum--to locate such things as underground water, hidden metal, buried treasure, oil, lost persons or golf balls, etc.

A particular claimant claims he can dowse for coal. A mutually agreed upon experiment was set up to test his claim. The set up of the experiment was as follows: The claimant may pick any person from a group of people to set up 11 identical empty containers and one container that contains coal (the type of container was mutually agreed upon). In other words, there were a total of 12 identical containers with only one that contained the coal. The claimant would then attempt to dowse for which container contains the coal. This experiment had been run 25 times; the total number of times the claimant got a "hit" was 5 times out of 25 attempts. With a 96% level of confidence, test the claim that the claimant was able to successfully detect coal at a proportion that is better than chance.

Set up the null and alternate hypotheses, determine the critical value, calculate the test statistic, select the correct decision, and select the correct "layperson's" statement for the conclusion.

If this test is a left tail test, use the negative answer for your critical value; otherwise use the positive value!

H₀:

p =p p

p p

H₁:

p =p p

p p

Critical Value = Test Statistic =

[Select Decision]We reject the null hypothesisWe fail to reject the null hypothesisWe accept the alternate hypothesis[Select Conclusion]With a 96% level of confidence, we can say the claimant was able to successfully detect coal at a proportion that is better than chance.There is not enough evidence to suggest the claimant was able to successfully detect coal at a proportion that is better than chance.

14. During an exit poll with 140 interviews, 84 people stated that they voted for Mike Crapo for the office of U.S. Senate from Idaho. Assuming that a candidate needs more than half of the votes cast in order to win, test the claim, with a 90% level of confidence, that it is likely that Mike Crapo won the election.

Set up the null and alternate hypotheses, determine the critical value, calculate the test statistic, select the correct decision, and select the correct "layperson's" statement for the conclusion.

If this test is a left tail test, use the negative answer for your critical value; otherwise use the positive value!

H₀:

p =p p

p p

H₁:

p =p p

p p

Critical Value = Test Statistic =

[Select Decision]We reject the null hypothesisWe fail to reject the null hypothesisWe accept the alternate hypothesis[Select Conclusion]With a 90% level of confidence, we can say it is likely that Mike Crapo won the election.There is not enough evidence to suggest it is likely that Mike Crapo won the election.

15. A small police agency conducted a "real conditions" test of their police officers. Under this test, an entire street scene was set up with many bystanders (actors) and a dangerous assailant; police officers were to seek out and find the dangerous assailant, decide whether or not to use their guns, and to fire their weapon if necessary. Instead of real ammunition, small round paint pellets were used and the officers and actors all wore appropriate protection. During the test, 141 rounds were fired by the police out of which 71 hit only the intended target. With a 94% level of confidence, test the claim that this police force has an accuracy rate of less than 65%.

Set up the null and alternate hypotheses, determine the critical value, calculate the test statistic, select the correct decision, and select the correct "layperson's" statement for the conclusion.

If this test is a left tail test, use the negative answer for your critical value; otherwise use the positive value!

H₀:

p =p p

p p

H₁:

p =p p

p p

Critical Value = Test Statistic =

[Select Decision]We reject the null hypothesisWe fail to reject the null hypothesisWe accept the alternate hypothesis[Select Conclusion]With a 90% level of confidence, we can say it is likely that this police force has an accuracy rate of less than 65%.There is not enough evidence to suggest it is likely that this police force has an accuracy rate of less than 65%.

16. Long term studies on kidney transplant recipients have shown that 52% of transplanted kidneys are still functioning after ten years. A new procedure is being developed to try to extend the ten year functionality rate of transplanted kidneys. A group of 123 patients were randamly selected for this new procedure and post surgery regimen. After ten years, 77 kidneys were still functioning correctly. With a 97% level of confidence, does it seem that there is enough evidence to suggest that this new technique for kidney transplants makes a difference in the ten year functionality of transplanted kidneys as compared to the old technique?

Set up the null and alternate hypotheses, determine the critical value, calculate the test statistic, select the correct decision, and select the correct "layperson's" statement for the conclusion.

If this test is a left tail test, use the negative answer for your critical value; otherwise use the positive value!

H₀:

p =p p

p p

H₁:

p =p p

p p

Critical Value = Test Statistic =

[Select Decision]We reject the null hypothesisWe fail to reject the null hypothesisWe accept the alternate hypothesis[Select Conclusion]With a 90% level of confidence, we can say this new technique for kidney transplants makes a difference in the ten year functionality of transplanted kidneysThere is not enough evidence to suggest this new technique for kidney transplants makes a difference in the ten year functionality of transplanted kidneys

17. A company that manufactures thingumabobs needs to determine whether or not their equipment needs to be recalibrated. The mean length of all thingumabobs that are produced must be 950 millimeters. A random sample of 74 thingumabobs was measured and the mean was determined to be 936.47 millimeters. If it is known that the population standard deviation for this process is 47.5, with a 90% level of confidence determine whether or not the equipment must be recalibrated.

Set up the null and alternate hypotheses, determine the critical value, calculate the test statistic, select the correct decision, and select the correct "layperson's" statement for the conclusion.

If this test is a left tail test, use the negative answer for your critical value; otherwise use the positive value!

H₀:

= < >

H₁:

= < >

Critical Value = Test Statistic =

[Select Decision]We reject the null hypothesisWe fail to reject the null hypothesisWe accept the alternate hypothesis[Select Conclusion]With a 90% level of confidence, we can say the equipment must be recalibrated.There is not enough evidence to suggest the equipment must be recalibrated.

18. Crazy Cola Company manufactures a soft drink named Morinaga Pancake Drink. They sell Morinaga Pancake Drink in 60 oz. bottles. A consumer advocacy group suspects that Crazy Cola is under filling its bottles and conducts a study to determine if their suspicions are founded by real statistical evidence. For this experiment, the advocacy group randomly selects a sample of 45 bottles and carefully measures the contents of each bottle. The mean of this sample was 58.77 oz. If it is known that the population standard deviation is 5.4 oz, with a 97% level of confidence, determine whether or not there is enough evidence to suggest that Crazy Cola is underfilling its bottles of Morinaga Pancake Drink.

Set up the null and alternate hypotheses, determine the critical value, calculate the test statistic, select the correct decision, and select the correct "layperson's" statement for the conclusion.

If this test is a left tail test, use the negative answer for your critical value; otherwise use the positive value!

H₀:

= < >

H₁:

= < >

Critical Value = Test Statistic =

[Select Decision]We reject the null hypothesisWe fail to reject the null hypothesisWe accept the alternate hypothesis[Select Conclusion]With a 97% level of confidence, we can say Crazy Cola is underfilling its bottles of Morinaga Pancake Drink.There is not enough evidence to suggest Crazy Cola is underfilling its bottles of Morinaga Pancake Drink.

19. Sweeney Todd, the owner Sweeney Todd's Barber Shop, claims that his shop has daily average revenues of $3000. The IRS decides to conduct an audit. For this audit, the IRS randomly selects 12 days in wich to observe the money transactions of the shop. The average daily revenue for Sweeney Todd's Barber Shop was determined to be $3165 with a standard deviation of $240. With a 95% level of confidence, determine if there's enough evidence to suggest that Mr. Todd is not reporting the shop's full revenue.

Set up the null and alternate hypotheses, determine the critical value, calculate the test statistic, select the correct decision, and select the correct "layperson's" statement for the conclusion.

If this test is a left tail test, use the negative answer for your critical value; otherwise use the positive value!

H₀:

= < >

H₁:

= < >

Critical Value = Test Statistic =

[Select Decision]We reject the null hypothesisWe fail to reject the null hypothesisWe accept the alternate hypothesis[Select Conclusion]With a 95% level of confidence, we can say Mr. Todd is not reporting the shop's full revenue.There is not enough evidence to suggest Mr. Todd is not reporting the shop's full revenue.

20. The General Electric Company is manufacturing a new ceramic jet engine for commercial jets--such as the Boeing 777. One advantage to using ceramic parts for jet engines is that the ceramics used weigh about 1/5 as much as conventional engines. One downside to ceramics is the tolerances used in production of ceramic parts are very small. For example, when a ceramic turbine is "fired" (a process of heating the ceramic at high temperatures for a period of time) the temperature in the kiln (oven) must be maintained at 4400^oF for several hours. If the firing temperature gets too hot, the ceramic might become too brittle for use in an engine; if the temperature is too cool, the ceramic will not maintain all it's properties necessary. Although a thermostat controls the temperature of the kiln, an operator must be present during the entire process in order to monitor the temperature and general firing process. The operator measures the temperature inside the kiln at random intervals; the temperature data is shown below. Assuming that an acceptable "firing"is one in which the average temperature is maintained at 4400^oF, with a 99% level of confidence, determine whether or not this "firing" isNOTrepresentative of a good firing for the manufacture of the ceramic turbine.

{4325, 4465, 4465, 4443, 4340, 4454, 4313, 4415, 4330}

Set up the null and alternate hypotheses, determine the critical value, calculate the test statistic, select the correct decision, and select the correct "layperson's" statement for the conclusion.

If this test is a left tail test, use the negative answer for your critical value; otherwise use the positive value!

H₀:

= < >

H₁:

= < >

Critical Value =

Test Statistic =

[Select Decision]We reject the null hypothesisWe fail to reject the null hypothesisWe accept the alternate hypothesis

[Select Conclusion]

NOT representative of a good firing." >With a 99% level of confidence, we can say this is NOT representative of a good firing.NOT representative of a good firing." >There is not enough evidence to suggest this is NOT representative of a good firing. 21. Based on Estimated Energy Requirements (EER) from the 2002 report of The Institute of Medicine (Dietary Reference Intakes Macronutrients Report), physically active women between the ages of 19 and 30 should consume healthy foods with a total calorie count of about 2000 calories. A study to determine the actual caloric intake of women in this age group had been conducted and the results, in calories taken in per day, are shown below. With a 95% level of confidence, determine if this study shows that physically active women, in this age group, do not seem to be consuming enough daily calories.

{1980, 1880, 1980, 1920, 2090, 1930, 1980, 1800}

Set up the null and alternate hypotheses, determine the critical value, calculate the test statistic, select the correct decision, and select the correct "layperson's" statement for the conclusion.

If this test is a left tail test, use the negative answer for your critical value; otherwise use the positive value!

H₀:

= < >

H₁:

= < >

Critical Value = Test Statistic =

[Select Decision]We reject the null hypothesisWe fail to reject the null hypothesisWe accept the alternate hypothesis[Select Conclusion]With a 95% level of confidence, we can say physically active women, in this age group, do not seem to be consuming enough daily calories.There is not enough evidence to suggest physically active women, in this age group, do not seem to be consuming enough daily calories.