I need the answers with work presented. Thank you.

1.

Find the critical value, Z/2, that corresponds to a confidence level of 87.12%

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 = 60, x = 24, with a(n) 91.8% 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 = 100, x = 20, with a(n) 84% level of confidence.

Type your answer in the form (lowerValue, upperValue)

4.

A survey of 40 randomly selected adults was conducted to determine if they thought college education should be a right for all who wish to attend. Out of the 40 people surveyed, 12 people thought college education should be a right for all who wish to attend. Determine the interval estimate of population proportion, p, with a confidence level of 87%.

Type your answer in the form (lowerValue, upperValue)

5.

A survey of 120 randomly selected adults asked the question "Do vaccines cause more health problems than they're worth?" Out of the 120 people surveyed, 60 people incorrectly answered "yes". Determine the interval estimate of population proportion of those people that incorrectly answered "yes" to the question "Do vaccines cause more health problems than they're worth?", with a confidence level of 95%.

Type your answer in the form (lowerValue, upperValue)

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 25.8% had answered the question correctly. At the 99% level of confidence, determine the minimum sample size necessary to estimate the interval estimate, within 4% 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 91% level of confidence, what minimum sample size is necessary to be to sure that the poll is within 3.5% of the population proportion of those that would answer "yes" to this question?

8.

A random sample of 62 primary care physicians' annual incomes was collected and the mean income was calculated to be $163000. It is known that the population standard deviation for this data is $11410. At the 82% level of confidence, construct the confidence interval about the population mean for this data.

Type your answer in the form (lowerValue, upperValue)

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 108 randomly selected customers determined that the mean wait time was 208 seconds with a standard deviation of 16.6 seconds. At the 90% level of confidence, construct the confidence interval about the population mean for this data.

Type your answer in the form (lowerValue, upperValue)

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.

{18, 20.25, 17.75, 9.75, 8.5, 18.5, 12, 19.25, 15.25, 6.5, 17.25, 14.25, 7.75, 13.25}

Type your answer in the form (lowerValue, upperValue)

11.

A survey of the price of doohickeys determined that when a random sample of 74 doohickeys had been collected, the price varied from $182.25 to $218.7 and the mean price was $194.58. With a 0.1 level of significance, construct the confidence interval about the population mean for the price of the doohickeys.

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 33 grams, at the 0.05 level of significance, Determine the minimum sample size necessary for this study. A pilot study by this researcher found standard deviation to be 291.98 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 silver. 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 9 identical empty containers and one container that contains silver (the type of container was mutually agreed upon). In other words, there were a total of 10 identical containers with only one that contained the silver. The claimant would then attempt to dowse for which container contains the silver. This experiment had been run 31 times; the total number of times the claimant got a "hit" was 7 times out of 31 attempts. With a 91% level of confidence, test the claim that the claimant was able to successfully detect silver 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:

H1:

Critical Value =

Test Statistic =

Decision:

Conclusion:

14.

During an exit poll with 160 interviews, 90 people stated that they voted for Dick Armey for the office of U.S. Representative from Texas. 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 Dick Armey 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:

H1:

Critical Value =

Test Statistic =

Decision:

Conclusion:

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, 133 rounds were fired by the police out of which 61 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:

H1:

Critical Value =

Test Statistic =

Decision:

Conclusion:

16.

Long term studies on kidney transplant recipients have shown that 55% 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 75 patients were randamly selected for this new procedure and post surgery regimen. After ten years, 48 kidneys were still functioning correctly. With a 92% 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:

H1:

Critical Value =

Test Statistic =

Decision:

Conclusion:

17.

A company that manufactures thingamajiggeries needs to determine whether or not their equipment needs to be recalibrated. The mean length of all thingamajiggeries that are produced must be 900 millimeters. A random sample of 54 thingamajiggeries was measured and the mean was determined to be 882.49 millimeters. If it is known that the population standard deviation for this process is 45, with a 91% 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 =

Decision:

Conclusion:

18.

Crazy Cola Company manufactures a soft drink named Crazy Cola. They sell Crazy Cola in 32 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 103 bottles and carefully measures the contents of each bottle. The mean of this sample was 31.45 oz. If it is known that the population standard deviation is 3.8 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 Crazy Cola.

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 =

Decision:

Conclusion:

19.

Sweeney Todd, the owner Sweeney Todd's Barber Shop, claims that his shop has daily average revenues of $2520. 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 $2657 with a standard deviation of $201.6. 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 =

Decision:

Conclusion:

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 2040oF 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 2040oF, with a 90% level of confidence, determine whether or not this "firing" is NOT representative of a good firing for the manufacture of the ceramic turbine.

{2005, 2042, 1997, 2013, 2068, 2007, 2050, 2083, 2065, 2029}

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 =

Decision:

Conclusion:

21.

Based on Estimated Energy Requirements (EER) from the 2002 report of The Institute of Medicine (Dietary Reference Intakes Macronutrients Report), physically active men between the ages of 19 and 30 should consume healthy foods with a total calorie count of about 2900 calories. A study to determine the actual caloric intake of men in this age group had been conducted and the results, in calories taken in per day, are shown below. With a 90% level of confidence, determine if this study shows that physically active men, in this age group, do not seem to be consuming enough daily calories.

{2530, 2520, 3070, 2580, 3010, 2830, 2640, 2880, 2670, 2930}

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 =

Decision:

Conclusion: