A random sample of 130 observations produced a mean of ?⎯⎯⎯=36.1x¯=36.1 from a population with a normal distribution and a standard deviation σ=4.87.

(a) Find a 95% confidence interval for μ
≤ μ ≤

(b) Find a 99% confidence interval for μ
≤ μ ≤

(c) Find a 90% confidence interval for μ
≤ μ ≤

Given are five observations for two variables, x and y. x i 1 2 3 4 5 y i 4 7 6 11 13 Round your answers to two decimal places. a. Using the following equation: Estimate the standard deviation of ŷ* when x = 3. b. Using the following expression: Develop a 95% confidence interval for the expected value of y when x = 3. to c. Using the following equation: Estimate the standard deviation of an individual value of y when x = 3. d. Using the following expression: Develop a 95% prediction interval for y when x = 3. If your answer is negative, enter minus (-) sign. to

The average number of words in a romance novel is 64,290 and the standard deviation is 17,422. Assume the distribution is normal. Let X be the number of words in a randomly selected romance novel. Round all answers to 4 decimal places where possible.

a. What is the distribution of X? X ~ N(___,____)

b. Find the proportion of all novels that are between 57,321 and 71,259 words. _____

c. The 95th percentile for novels is ____ words. (Round to the nearest word)

d. The middle 50% of romance novels have from ____words to_____ words. (Round to the nearest word)

find the sample size needed to give with 99% confidence a margin of error of plus or minus 5% when estimating proportion within plus minus 4% within plus minus 1%

The mean output of a certain type of amplifier is 496 watts with a variance of 144. If 40 amplifiers are sampled, what is the probability that the mean of the sample would differ from the population mean by less than 1.2 watts? Round your answer to four decimal places.

The College Board wanted to test whether students graduating from private colleges and students graduating from public universities had different amounts of student loan debt. A sample of students from 146 private colleges across the country yielded an average loan debt of $29,972 with a standard deviation of $3,200. A sample of students from 225 public universities yielded an average loan debt of $28,762 with a standard deviation of $5,600. Conduct the test at the α=0.02α=0.02 level of significance.

What is meant by an absolute effect in epidemiologic research? Present at least one relevant example.

The mean cost of domestic airfares in the United States rose to an all-time high of $380 per ticket. Airfares were based on the total ticket value, which consisted of the price charged by the airlines plus any additional taxes and fees. Assume domestic airfares are normally distributed with a standard deviation of $100. Use Table 1 in Appendix B.

a. What is the probability that a domestic airfare is $545 or more (to 4 decimals)?

b. What is the probability that a domestic airfare is $255 or less (to 4 decimals)?

c. What if the probability that a domestic airfare is between $320 and $490 (to 4 decimals)?

d. What is the cost for the 5% highest domestic airfares? (rounded to nearest dollar)

19. Assume that females have pulse rates that are normally distributed with a mean of mu equals 74.0 beats per minute and a standard deviation of sigma equals 12.5 beats per minute. Complete parts​ (a) through​ (c) below.

a. If 1 adult female is randomly​ selected, find the probability that her pulse rate is between 70 beats per minute and 78 beats per minute.

The probability is _____

​(Round to four decimal places as​ needed.)

b. If 4 adult females are randomly​ selected, find the probability that they have pulse rates with a mean between 70 beats per minute and 78 beats per minute.

The probability is____

​(Round to four decimal places as​ needed.)

c. Why can the normal distribution be used in part​ (b), even though the sample size does not exceed​ 30?

A.Since the original population has a normal​ distribution, the distribution of sample means is a normal distribution for any sample size.

B.Since the distribution is of​ individuals, not sample​ means, the distribution is a normal distribution for any sample size.

C.Since the mean pulse rate exceeds​ 30, the distribution of sample means is a normal distribution for any sample size.

D.Since the distribution is of sample​ means, not​ individuals, the distribution is a normal distribution for any sample size.

20. An elevator has a placard stating that the maximum capacity is 2310 lb -15 passengers. ​ So, 15 adult male passengers can have a mean weight of up to 2310 divided by 15 equals 154 pounds. If the elevator is loaded with 15 adult male​ passengers, find the probability that it is overloaded because they have a mean weight greater than 154 lb.​ (Assume that weights of males are normally distributed with a mean of 163 lb and a standard deviation of 31 lb​.) Does this elevator appear to be​ safe?

The probability the elevator is overloaded is_____

​(Round to four decimal places as​ needed.)

Does this elevator appear to be​ safe?

A.No, there is a good chance that 15 randomly selected people will exceed the elevator capacity.

B.Yes, there is a good chance that 15 randomly selected people will not exceed the elevator capacity.

C.Yes, 15 randomly selected people will always be under the weight limit.

D.No, 15 randomly selected people will never be under the weight limit.

The world is full of misleading messages. Many of them are comming from the fact that people do not know how to interpret data. Find an example of a misleading use of statistics in a newspaper, magazine, corporate annual report, or other source. Then explain why your example is misleading.

TABLE 6-4

According to Investment Digest, the arithmetic mean of the annual return for common stocks from 1926-2010 was 9.5% but the value of the variance was not mentioned. Also 25% of the annual returns were below 8% while 65% of the annual returns were between 8% and 11.5%. The article claimed that the distribution of annual return for common stocks was bell-shaped and approximately symmetric. Assume that this distribution is normal with the mean given above. Answer the following questions without the help of a calculator, statistical software, or statistical table.

15) Referring to Table 6-4, find the probability that the annual return of a random year will be less than 11.5%.____?

16) Referring to Table 6-4, find the probability that the annual return of a random year will be more than 11.5%_____?

17) Referring to Table 6-4, find the probability that the annual return of a random year will be between 7.5% and 11%.________?

18) Referring to Table 6-4, what is the value above which will account for the highest 25% of the possible annual returns?_________

19) Referring to Table 6-4, 75% of the annual returns will be lower than what value?___________

1. 
   
2. You are a public health nurse working in an elementary school in Hamilton, Ontario. You have seen a substantial increase in the number of children in your school presenting with Attention Deficit Disorder (ADD). You are interested in whether a new drug developed by a local drug company improves the ability of children with ADD to maintain attention. You obtain ethics approval to study the drug, informed consent from the parents of 24 fifth grade children with ADD, administer the drug to the 24 children, and administer a test to the children to determine their ability to maintain attention while performing a task. Scores are continuous, can range from 0 to 25 with higher scores reflecting a better ability to maintain attention, and you know from previous research that scores tend to be normally distributed. Six of these students receive a placebo containing none of the drug. Six students receive 2 mg of the drug, six students receive 4 mg of the drug, and six students receive 6 mg of the drug. The table below summarizes the results from your study. Use these data to answer the following questions. Assume α=0.05.

3. Placebo (0 mg)	Drug (2 mg)	Drug (4 mg)	Drug (6 mg)
   4	7	16	17
   7	8	14	18
   11	13	12	13
   11	6	11	17
   7	9	15	20
   10	9	13	15

4. a.You have one further prediction, and that is that children with ADD who receive the drug will perform significantly better than children with ADD who do not receive the drug. Conduct the appropriate test to confirm this prediction, if the results from question a support doing this additional testing. Are you able to confirm your prediction? Explain, including the calculations and/or SPSS output to support your answer. [2 Marks]

Overproduction of uric acid in the body can be an indication of cell breakdown. This may be an advance indication of illness such as gout, leukemia, or lymphoma.† Over a period of months, an adult male patient has taken twelve blood tests for uric acid. The mean concentration was x = 5.35 mg/dl. The distribution of uric acid in healthy adult males can be assumed to be normal, with σ = 1.87 mg/dl.

(a) Find a 95% confidence interval for the population mean concentration of uric acid in this patient's blood. (Round your answers to two decimal places.)

lower limit
upper limit
margin of error

(b) What conditions are necessary for your calculations? (Select all that apply.)

uniform distribution of uric acidn is largenormal distribution of uric acidσ is knownσ is unknown

(c) Give a brief interpretation of your results in the context of this problem.

There is a 5% chance that the confidence interval is one of the intervals containing the population average uric acid level for this patient.There is not enough information to make an interpretation.     The probability that this interval contains the true average uric acid level for this patient is 0.05.The probability that this interval contains the true average uric acid level for this patient is 0.95.There is a 95% chance that the confidence interval is one of the intervals containing the population average uric acid level for this patient.

(d) Find the sample size necessary for a 95% confidence level with maximal error of estimate E = 1.08 for the mean concentration of uric acid in this patient's blood. (Round your answer up to the nearest whole number.)
blood tests

The 90 students in a statistics class are categorized by gender and by the year in school. The numbers are listed in the following table:

Year in School	Freshman	Sophmore	Junior	Senior
Gender
Male	1	4	8	17
Female	23	17	13	7

Test the null hypothesis that there is no association between the year in school and the gender using a 1% significance level. Be sure to specify the test statistic with degrees of freedom, the P-value or critical value, and your conclusion. Please no computer software answers! Thank you!

At Burnt Mesa Pueblo, archaeological studies have used the method of tree-ring dating in an effort to determine when prehistoric people lived in the pueblo. Wood from several excavations gave a mean of (year) 1239 with a standard deviation of 43 years. The distribution of dates was more or less mound-shaped and symmetrical about the mean. Use the empirical rule to estimate the following.

(a) a range of years centered about the mean in which about 68% of the data (tree-ring dates) will be found
between  and  A.D.

(b) a range of years centered about the mean in which about 95% of the data (tree-ring dates) will be found
between  and  A.D.

(c) a range of years centered about the mean in which almost all the data (tree-ring dates) will be found
between  and  A.D.