(9). The National Health Statistics Reports dated Oct. 22, 2008, stated that for a sample size of 277 18-year-old American males, the sample mean waist circumference was 86.3 cm. A somewhat complicated method was used to estimate various population percentiles, resulting in the following values.

5^th   10^th   25^th  50^th 75^th 90^th 95^th

69.6 70.9 75.2 81.3 95.4 107.1 116.4

(a) Is it plausible that the waist size distribution is at least approximately normal? Explain your reasoning.

1. Since the mean and median are substantially different, and the difference in the distance between the median and the upper quartile and the distance between the median and the lower quartile is relatively large, it seems plausible that waist size is at least approximately normal.
2. Since the mean and median are nearly identical, and the distance between the median and the upper quartile and the distance between the median and the lower quartile are almost the same, it does not seem plausible that waist size is at least approximately normal.
3. Since the mean and median are nearly identical, and the distance between the median and the upper quartile and the distance between the median and the lower quartile are nearly the same, it seems plausible that waist size is at least approximately normal.
4. Since the mean and median are substantially different, and the distance between the median and the upper quartile and the distance between the median and the lower quartile are nearly the same, it seems plausible that waist size is at least approximately normal.
5. Since the mean and median are substantially different, and the difference in the distance between the median and the upper quartile and the distance between the median and the lower quartile is relatively large, it does not seem plausible that waist size is at least approximately normal.

(b)   Make a conjecture on the shape of the population distribution.

1. The upper percentiles stretch much farther than the lower percentiles. Therefore, we might suspect a right-skewed distribution.
2. The lower percentiles stretch much farther than the upper percentiles. Therefore, we might suspect a right-skewed distribution.     
3. The upper percentiles stretch much farther than the lower percentiles. Therefore, we might suspect a left-skewed distribution.
4. The lower percentiles stretch much farther than the upper percentiles. Therefore, we might suspect a left-skewed distribution.
5. It is plausible that waist size is at least approximately normal.

(C)    Suppose that the population mean waist size is 85 cm and that the population standard deviation is 15 cm. How likely is it that a random sample of 277 individuals will result in a sample mean waist size of at least 86.3 cm? (Round your answers to four decimal places.)

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(d)    Referring back to (C), suppose now that the population mean waist size in 82 cm. Now what is the (approximate) probability that the sample mean will be at least 86.3 cm? (Round your answers to three decimal places.)

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(e)     In light of this calculation, do you think that 82 cm is a reasonable value for μ?

1. No 82 cm is not a reasonable value for μ since if the population mean waist size is 82 cm, there would be almost no chance of observing a sample mean waist size of 86.3 cm (or higher) in a random sample of 277 men.
2. Yes 82 cm is a reasonable value for μ since if the population mean waist size is 82 cm, there would be almost no chance of observing a sample mean waist size of 86.3 cm (or higher) in a random sample of 277 men.    
3. Yes 82 cm is a reasonable value for μ since it is almost the same as 50^th percentile 81.3.
4. Yes 82 cm is a reasonable value for μ since if the population mean waist size is 82 cm, there is a reasonably large chance of observing a sample mean waist size of 86.3 cm (or higher) in a random sample of 277 men.
5. No 82 cm is not a reasonable value for μ since if the population mean waist size is 82 cm, there is a reasonably large chance of observing a sample mean waist size of 86.3 cm (or higher) in a random sample of 277 men.

You and a friend, along with an eccentric rich probabilist, are observing a Poisson process whose arrival rate is λ = .5 per hour. The probabilist offers to pay you $100 if there is at least one arrival between noon and 2pm, and also offers to pay your friend $100 if there is at least one arrival between 1pm and 3pm.

a. What is the probability that either you or your friend, or both, gets $100?

b. What is the probability that one of you wins $100, but not both?

Consider a Poisson process with arrival rate λ per minute. Given that there were three arrivals in the first 2 minutes, find the probability that there were k arrivals in the first minute; do this for k = 0, 1, 2, and 3.

Given that P(A) = .4, P(A ∩ B) = .1, and P((A ∪ B) c ) = .2, find P(B).

13. Using traditional methods, it takes 94 hours to receive a basic flying license. A new license training method using Computer Aided Instruction (CAI) has been proposed. A researcher used the technique with 210 students and observed that they had a mean of 95 hours. Assume the standard deviation is known to be 5. A level of significance of 0.05 will be used to determine if the technique performs differently than the traditional method. Is there sufficient evidence to support the claim that the technique performs differently than the traditional method?

What is the conclusion?

A. There is not sufficient evidence to support the claim that the technique performs differently than the traditional method.

B. There is sufficient evidence to support the claim that the technique performs differently than the traditional method.

14. Using traditional methods it takes 90 hours to receive an advanced driving license. A new training technique using Computer Aided Instruction (CAI) has been proposed. A researcher believes the new technique may reduce training time and decides to perform a hypothesis test. After performing the test on 190 students, the researcher decides to reject the null hypothesis at a 0.02 level of significance.

What is the conclusion?

A. There is sufficient evidence at the 0.020 level of significance that the new technique reduces training time.

B. There is not sufficient evidence at the 0.02 level of significance that the new technique reduces training time.

Suppose 56% of the population has a college degree. If a random sample of size 503 is selected, what is the probability that the proportion of persons with a college degree will be greater than 54%? Round your answer to four decimal places.

In one of PLE’s manufacturing facilities, a drill press that has three drill bits is used to fabricate metal parts. Drill bits break occasionally and need to be replaced. The present policy is to replace a drill bit when it breaks or can no longer be used. The operations manager is considering a different policy in which all three drill bits are replaced when any one bit breaks or needs replacement. The rationale is that this would reduce downtime. It costs $200 each time the drill press must be shut down. A drill bit costs $85, and the variable cost of replacing a drill bit is $14 per bit. The company that supplies the drill bits has historical evidence that the reliability of a single drill bit is describes by a Poisson probability distribution with the mean time between failures is an exponential distribution with mean μ = 1 / λ = 1 / 0.01 = 100 hours. (Professor Cursio: see below.) The operations manager at PLE would like to compare the cost of the two replacement policies. Develop spreadsheet models to determine the total cost for each policy over 1,000 hours and make a recommendation. Explain and summarize your findings in a report

Suppose data made available through a health system tracker showed health expenditures were $10,348 per person in the United States. Use $10,348 as the population mean and suppose a survey research firm will take a sample of 100 people to investigate the nature of their health expenditures. Assume the population standard deviation is $2,500.

What is the probability the sample mean will be within ±$150 of the population mean? (Round your answer to four decimal places.)

The results of a​ two-way ANOVA using the accompanying data and hypothesis tests for interaction between Factor A and Factor B and for each factor are provided below. Using these data and​ results, determine which means are different using α= 0.01when warranted.

Are the means for Factor​ A, Level 1 and Factor​ A, Level 2 significantly​ different?

A.Yes

B. No

C.The comparison is unwarranted because there is insufficient evidence to conclude that not all Factor A means are equal.

D.The comparison is unwarranted because Factor A and Factor B interact.

Are the means for Factor​ A, Level 1 and Factor​ A, Level 3 significantly​ different?

A.Yes

B. No

C.The comparison is unwarranted because there is insufficient evidence to conclude that not all Factor A means are equal.

D.The comparison is unwarranted because Factor A and Factor B interact.

Are the means for Factor​ A, Level 2 and Factor​ A, Level 3 significantly​ different?

A.Yes

B.No

C.The comparison is unwarranted because there is insufficient evidence to conclude that not all Factor A means are equal.

D.The comparison is unwarranted because Factor A and Factor B interact.

Are the means for Factor​ B, Level 1 and Factor​ B, Level 2 significantly​ different?

A.Yes

B.No

C.The comparison is unwarranted because there is insufficient evidence to conclude that not all Factor B means are equal.

D.The comparison is unwarranted because Factor A and Factor B interact.

Are the means for Factor​ B, Level 1 and Factor​ B, Level 3 significantly​ different?

A.No

B.Yes

C.The comparison is unwarranted because there is insufficient evidence to conclude that not all Factor B means are equal.

D.The comparison is unwarranted because Factor A and Factor B interact.

Are the means for Factor​ B, Level 2 and Factor​ B, Level 3 significantly​ different?

A.No

B.Yes

C.The comparison is unwarranted because there is insufficient evidence to conclude that not all Factor B means are equal.

D.The comparison is unwarranted because Factor A and Factor B interact.

The survival times in days of 72 guinea pigs after they were injected with infectious bacteria in a medical experiment is displayed in the table.

To access the complete data set, click the link for your preferred software format:

Excel  Minitab  JMP  SPSS TI  R  Mac-TXT   PC-TXT  CSV CrunchIt!

(a) Use the software of your choice to graph the distribution and describe its main features. Select the best description from the given choices.

The distribution is strongly left‑skewed, with the center around 100 days and a range from about 0 days to about 600 days.

The distribution is strongly right‑skewed, with the center around 100 days and a range from about 0 days to about 600 days.

The distribution is bimodal, with the center around 100 days and a range from about 0 days to about 600 days.

The distribution is Normal, with the center around 300 days and a range from about 0 days to about 600 days.

(b) Use the software of your choice to calculate the five‑number summary for these data. (Enter your answers rounded to one decimal place.)

Min=

days

?1=

days

Median=

days

?3=

days

Max=

days

Calculate the mean for these data. (Enter your answer rounded to one decimal place.)

mean=

days

Summarize your findings. Choose the best statement.

The median is closer to ?1 than to ?3

The mean and the median are almost equal.

The median is closer to ?3 than to ?1

The mean is closer to ?1 than to ?3

1. Assume that a researcher is interested in finding out the relationship between standardized test scores and household income. Seven participants have been randomly selected and their ACT Composite score and household income are reported. By performing a test, can you conclude that there is a significant relationship between household income and ACT Composite score? State your null and alternative hypotheses. Please show all of the required steps. Use the data in the table below. Assume α = .05 (20 points)

The owner of Maumee Ford-Volvo wants to study the relationship between the age of a car and its selling price. Listed below is a random sample of 12 used cars sold at the dealership during the last year.

1. Determine the regression equation. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)

2. Estimate the selling price of an 7-year-old car (in $000). (Round your answer to 3 decimal places.)

3. Interpret the regression equation (in dollars). (Round your answer to the nearest dollar amount.)

(A) If the answer in (c) is greater than 0.01 then we conclude at the 1% significance
level that the average weight of a bear in Yellowstone National Park is different from 187 lb.

(B) If the answer in (c) is less than 0.01 then we cannot conclude at the 1% significance
level that the average weight of a bear in Yellowstone National Park is different from 187 lb.

(C) If the answer in (a) is greater than the answer in (b) then we cannot conclude at the 1% significance
level that the average weight of a bear in Yellowstone National Park is different from 187 lb.

(D) If the answer in (c) is less than 0.01 then we conclude at the 1% significance
level that the average weight of a bear in Yellowstone National Park is different from 187 lb.

(E) If the answer in (a) is greater than the answer in (c) then we cannot conclude at the 1% significance
level that the average weight of a bear in Yellowstone National Park is different from 187 lb.

(F) If the answer in (b) is greater than the answer in (c) then we cannot conclude at the 1% significance
level that the average weight of a bear in Yellowstone National Park is different from 187 lb.

(G) If the answer in (a) is greater than the answer in (c) then we conclude at the 1% significance
level that the average weight of a bear in Yellowstone National Park is different from 187 lb.

(H) If the answer in (b) is greater than the answer in (c) then we conclude at the 1% significance
level that the average weight of a bear in Yellowstone National Park is different from 187 lb.

For each of the following statements, list the independent and dependent variables, and give the research hypothesis and the null hypothesis.

An official at the state transportation office thinks that switching over from manual to automated toll collection will decrease administrative costs, and asks you to do a survey of other states costs and collection practices to determine if this is true.

The local firefighter’s union in your town claims that its salaries are lower than those of firefighters in other towns.

A legal advocacy group charges that local cops are pulling over Black drivers at higher rates than White drivers.

A official claim that the recent decrease in crime can be attributed to the city’s new neighborhood watch program

Some people are concerned that new tougher standards and​ high-stakes tests adopted in many states have driven up the high school dropout rate. The National Center for Education Statistics reported that the high school dropout rate for the year 2014 was 6.5​%. One school district whose dropout rate has always been very close to the national average reports that 125 of their 1767 high school students dropped out last year. Is this evidence that their dropout rate may be​ increasing? Explain.

Compute the test statistic?

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

What is the P-value

(A) Discuss the probability of landing on heads if you flipped a coin 10 times?

(B) What is the probability the coin will land on heads on each of the 10 coin flips?

(C) Apply this same binomial experiment to a different real-world situation. Describe a situation involving probability?

please explain each and show work. showing the steps to the answer would be great..