Use the accompanying paired data consisting of registered boats​ (tens of​ thousands) and manatee fatalities from boat encounters. Let x represent the number of registered boats and let y represent the corresponding number of manatee deaths. Use the given number of registered boats and the given confidence level to construct a prediction interval estimate of manatee deaths. Use x=89 (for 89​0,000 registered​ boats) with a 99​% confidence level.

Boats (tens of thousands)   Manatees
67    54
68    37
66    34
73    49
74    40
70    59
76    56
82    67
83    84
83    80
90    82
91    94
95   74
93   69
97   78
99   93
97   73
98   91
98   97
91   81
90   87
90   82
89   73
90   7

Find the indicated prediction interval.

___manatees < y < manatees

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

A dairy scientist is testing a new feed additive. She chooses 13 cows at random from a large population. She randomly assigns n_old = 8 to the old diet and n_new = 5 to a new diet including the additive. The cows are housed in 13 widely separated pens. After two weeks, she milks each cow and records the milk produced in pounds:

Old Diet: 43, 51, 44, 47, 38, 46, 40, 35 New Diet: 47, 75, 85, 100, 58

Let μnew and μold be the population mean milk productions for the new and old diets, respectively. She wishes to test H0 : μnew − μold = 0 against HA : μnew − μold ̸= 0 using α = 0.05.

(a) Graph the data as you see fit. Why did you choose the graph(s) that you did and what does it (do they) tell you?

(b) Choose a test appropriate for the hypotheses and justify your choice based on your answer to part (a). Then perform the test by computing a p-value, and making a reject or not reject decision. Do this without R and show your work. (Also do it with R, if you wish, to check your work). Finally, state your conclusion in the context of the problem.

n a 2008​ survey, people were asked their opinions on astrology​ - whether it was very​ scientific, somewhat​ scientific, or not at all scientific. Of 1438 who​ responded, 76 said astrology was very scientific. a. Find the proportion of people in the survey who believe astrology is very scientific. b. Find a​ 95% confidence interval for the population proportion with this belief. c. Suppose a TV news anchor said that​ 5% of people in the general population think astrology is very scientific. Would you say that is​ plausible? Explain your answer. a. The proportion of people in the survey who believe astrology is very scientific is . 0529. ​(Round to four decimal places as​ needed.) b. Construct the​ 95% confidence interval for the population proportion with the belief that astrology is very scientific. left parenthesis nothing comma nothing right parenthesis ​(Round to three decimal places as​ needed.) Enter your answer in the edit fields and then click Check Answer.

Consider two random variables X and Y, with Y = (a+bX)

- Find E(Y)

- Find Cov(X,Y)

- Find Corr(X,Y)

(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.)

________________________________________________________________

(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.)

________________________________________________________________

(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.)