In this problem, assume that the distribution of differences is approximately normal. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value by a small amount and therefore produce a slightly more "conservative" answer.

At five weather stations on Trail Ridge Road in Rocky Mountain National Park, the peak wind gusts (in miles per hour) for January and April are recorded below.

What is the value of the sample test statistic? (Round your answer to three decimal places.)
In this problem, assume that the distribution of differences is approximately normal. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value by a small amount and therefore produce a slightly more "conservative" answer.

What is the value of the sample test statistic? (Round your answer to three decimal places.)

In this problem, assume that the distribution of differences is approximately normal. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value by a small amount and therefore produce a slightly more "conservative" answer.

Are America's top chief executive officers (CEOs) really worth all that money? One way to answer this question is to look at row B, the annual company percentage increase in revenue, versus row A, the CEO's annual percentage salary increase in that same company. Suppose a random sample of companies yielded the following data:

Do these data indicate that the population mean percentage increase in corporate revenue (row B) is different from the population mean percentage increase in CEO salary? Use a 5% level of significance. (Let d = B − A.)

What is the value of the sample test statistic? (Round your answer to three decimal places.)

In this problem, assume that the distribution of differences is approximately normal. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value by a small amount and therefore produce a slightly more "conservative" answer.

Is fishing better from a boat or from the shore? Pyramid Lake is located on the Paiute Indian Reservation in Nevada. Presidents, movie stars, and people who just want to catch fish go to Pyramid Lake for really large cutthroat trout. Let row B represent hours per fish caught fishing from the shore, and let row A represent hours per fish caught using a boat. The following data are paired by month from October through April.

Use a 1% level of significance to test if there is a difference in the population mean hours per fish caught using a boat compared with fishing from the shore. (Let d = B − A.)

What is the value of the sample test statistic? (Round your answer to three decimal places.)

A pollster claims that Socialist proportion of registered Socialist voters in his country is lower than 0.05. A random sample of size 1000 registered voters revealed that the number of Socialists was 40. Test the relevant hypotheses at the 1% significance level.

Greatest president ~ A Gallup Poll of 1800 American adults in February 2009 asked the following question. "Which of the following presidents would you regard as the greatest: Washington, Franklin Roosevelt, Lincoln, Kennedy, or Reagan?" The order of the presidents was rotated to avoid bias. Based on the sample, a 95% confidence interval for the actual proportion American adults who choose Lincoln as the greatest is given by (0.1122, 0.2211).Which of the following statements are true? Select all the that apply.

A 99% confidence interval calculated using the same data will include more plausible values for the actual population proportion.

If the sample size had been double the sample size in the scenario above, then the 95% confidence interval would be half as wide as the one stated above.

If a different sample of the same size were to be selected, then there is a 95% chance that the new sample proportion will lie inside the confidence interval stated above.

If we took several samples of the same size as the scenario given above and constructed 95% confidence intervals for population proportion, then it is reasonable to expect 95% of these confidence intervals to contain the actual population proportion.

A 90% confidence interval for the population proportion calculated using the same data will be wider than the interval stated above.

If a different sample of the same size were to be selected and a 95% confidence interval constructed, then there is a 95% chance that the actual population proportion will lie inside the new confidence interval.

Suppose passengers arrive at the MTA train station following a Poisson distribution with parameter 9 and the unit of time 1 hour.

Next train will arrive either 1 hour from now or 2 hours from now, with a 50/50 probability.

i. E(train arrival time)

ii. E(number of people who will board the train)

iii. var(number of people who will board the train)

The Federal Reserve reports that the mean lifespan of a five dollar bill is 4.9 years. Let's suppose that the standard deviation is 2.1 years and that the distribution of lifespans is normal (not unreasonable!)

Find:

(a) the probability that a $5 bill will last more than 4 years.

(b) the probability that a $5 bill will last between 5 and 7 years.

(c) the 94th percentile for the lifespan of these bills (a time such that 94% of bills last less than that time).

(d ) the probability that a random sample of 37 bills has a mean lifespan of more than 5.1 years.

Using R Studio/R programming...

A consumer-reports group is testing whether a gasoline additive changes a car's gas mileage. A test of seven cars finds an average improvement of 0.4 miles per gallon with a standard deviation of 3.57. Is the difference significantly greater than 0? Assume that the values are normally distributed.

What would the code be?

A random sample of 50 suspension helmets used by motorcycle riders and automobile race-car drivers was subjected to an impact test, and on 18 of these helmets some damage was observed.

(a)Test the hypotheses H0: p = 0.3 versus H1: p ≠ 0.3 with α = 0.05, using the normal approximation.

(b)Find the P-value for this test.

(c)Find a 95% two-sided confidence interval on the true proportion of helmets of this type that would show damage from this test. Explain how this confidence interval can be used to test the hypothesis in part (a).

(d)Using the point estimate of p obtained from the preliminary sample of 50 helmets, how many helmets must be tested to be 95% confident in order to keep the associated β-error at 0.1 (or the power at 90%)?

11-14 Highland Automotive wishes to forecast the number

of new cars that will be sold next week. The following

table summarizes the number of new cars sold

during each of the past 12 weeks: (PLEASE ANSWER BY USING EXCEL)

(a) Provide a forecast by using a 3-week weighted

moving average technique with weights 5, 3, and

1 (5 = most recent).

(b) Forecast sales by using an exponential smoothing

model with a = 0.45.

(c) Highland would like to forecast sales by using

linear trend analysis. What is the linear equation

that best fits the data?

(d) Which of the methods analyzed here would you

use? Explain your answer.

1. SAT math scores are normally distributed with a mean 525 and a standard deviation of 102. In order to qualify for a college you are interested in attending your SAT math score must be in the highest 9.34% of all SAT scores. What is the minimum score you need on the SAT to qualify for the college?

2. If you get into this college you are interested in running for the track team. To qualify for the track team you must run in the fastest 4.75% of all runners of the mile. If the running of the mile is normally distributed with a mean of 6.02 minutes and a standard deviation of 1.32 minutes what is the maximum time you have to run the mile and still qualify for the team?

3. The time a cell phone lasts until it needs to be recharged is normally distributed with a mean of 14 hours and a standard deviation of 3 hours.

a) You have to have your cell phone work for 10 hours as you are going on a hike. What is the probability the cell phone will not make the 10 hours necessary? (in other words what % cell phones last 10 hours or less before needing to be recharged)?

b) What percent of cell phones last over 18 hours before they have to be recharged?

How long does it take to commute from home to​ work? It depends on several factors including the​ route, traffic, and time of departure. These times tend to be fairly close to symmetrical and​ mound-shaped. The data listed below​ (in minutes) is for a random sample of eight trips. Construct a

95​%

confidence interval for the population mean time of all such commutes.

26    

39    

34    

44    

20    

36    

31    

39

​A) What is the mean for this set of​ data? 

​B) Confidence​ Interval: (

nothing

​,

nothing

​)

​(round all answers to two decimal​ places)

​C) The mean commute for professor St. John is 45 minutes. Does she have the same commute as the​ population?

A.

She has the same commute because 45 is the same as the sample mean.

B.

She does not have the same commute because 45 is not the same as the sample mean.

C.

She does not have the same commute because 45 is not within the interval.

D.

She has the same commute because 45 is within the interval.

The mean time taken to design a house plan by 39 architects was found to be 17 hours with a standard deviation of 3.25 hours.

Construct a 98% confidence interval for the population mean μ.


Round your answers to two decimal places.

_____to_____  hours

Suppose the average speeds of passenger trains traveling from Newark, New Jersey, to Philadelphia, Pennsylvania, are normally distributed, with a mean average speed of 88 miles per hour and a standard deviation of 6.4 miles per hour.

(a) What is the probability that a train will average less than 72 miles per hour?

(b) What is the probability that a train will average more than 80 miles per hour?

(c) What is the probability that a train will average between 91 and 99 miles per hour?

(Round the values of z to 2 decimal places. Round your answers to 4 decimal places.)

(a) P(x < 72)=???

(b) P(x > 80)=???

(c) P(91 ≤ x ≤ 99)=???

A company samples the distribution of conductivity in isolation of receptacles and got the following values:

24.46 25.61 26.25 26.42 26.66 27.15 27.31 27.54 27.74 27.94 27.98 28.04 28.28 28.49 28.50 28.87 29.11 29.13 29.50 30.88

Trimming 10% mean when we discard the smallest and largest 10 % of the sample. Can we use that sample for to calculate the point estimate of population mean? What are the values for estimator of population mean with and without trim? Provide full reasoning.