1) Let X be a continuous random variable. What is true about fX(x)fX(x)?
fX(2) is a probability.
fX(2) is a set.
It can only take values between 0 and 1 as input.
fX(2) is a number.

2) Let X be a continuous random variable. What is true about FX(x)FX(x)?
FX(x) is a strictly increasing function.
It decreases to zero as x→∞x→∞.
FX(2) is a probability.
FX(x) can be any real number.

Engineers concerned about a tower's stability have done extensive studies of its increasing tilt. Measurements of the lean of the tower over time provide much useful information. The following table gives measurements for the years 1975 to 1987. The variable "lean" represents the difference between where a point on the tower would be if the tower were straight and where it actually is. The data are coded as tenths of a millimeter in excess of 2.9 meters, so that the 1975 lean, which was 2.9646 meters, appears in the table as 646. Only the last two digits of the year were entered into the computer.

Year	75	76	77	78	79	80	81	82	83	84	85	86	87
Lean	646	648	660	670	676	691	700	701	717	721	728	745	761

(a) Plot the data. Consider whether or not the trend in lean over time appears to be linear. (Do this on paper. Your instructor may ask you to turn in this graph.)

(b) What is the equation of the least-squares line? (Round your answers to three decimal places.)
y =  +  x

What percent of the variation in lean is explained by this line? (Round your answer to one decimal place.)
%

(c) Give a 99% confidence interval for the average rate of change (tenths of a millimeter per year) of the lean. (Round your answers to two decimal places.)
( , )

Use technology and the given confidence level and sample data to find the confidence interval for the population mean μ. Assume that the population does not exhibit a normal distribution. Weight lost on a diet: 99% confidence n=41 x overbar =4.0 kg s=6.9 kg What is the confidence interval for the population mean μ? ___ kg<μ<___ kg (Round to one decimal place as needed.) Is the confidence interval affected by the fact that the data appear to be from a population that is not normally distributed? A. No, because the population resembles a normal distribution. B. No, because the sample size is large enough. C. Yes, because the population does not exhibit a normal distribution. D. Yes, because the sample size is not large enough.

Scores on a certain IQ test are known to have a mean of 100. A random sample of 60 students attend a series of coaching classes before taking the test. Let m be the population mean IQ score that would occur if every student took the coaching classes. The classes are successful if m > 100. A test is made of the hypotheses H0: m = 100 vs H1: m > 100.

Consider three possible conclusions:

The classes are successful.

The classes are not successful.

The classes might not be successful.

Answer the following questions:

1.Which of the three conclusions is best if H0 is rejected?

2.Which of the three conclusions is best if H0 is not rejected?

3.Assume that the classes are successful but the conclusion is reached that the classes might not be successful. Which type of error is this?

4.Assume that the classes are not successful. Is it possible to make a Type I error? Explain.

5.Assume that the classes are not successful. Is it possible to make a Type II error? Explain.

I have draw a random sample of 20 of my neighbors. I ask them their income (What can I say? I'm a nosy neighbor). My sample average (x bar) is $41,000. I want to create a 95% confidence interval around x bar.

My estimated standard deviation is $5,000.

What is the 95% confidence internal for the average income in my neighborhood? $38,652 to $43.347, $38,663 to $43,336, $38,809 to $43,191, or not enough information?

What are ALL the possible difficulties with with fitting linear regression? Please explain the reasoning.

Read the essay: The Median Isn’t the Message

by Stephen Jay Gould and answer the following discussion question.

Explain why it is preferable for someone in the better half that the distribution of the survival

variable is right skewed, not left skewed.?

Minium 150-200 words: Why is a confidence interval better than a point estimate? Provide an example

1. a. Assume that Data Set A depicts the scores of 10 subjects who received either Treatment 1 or Treatment 2. Calculate a t-test for independent means to determine whether the means are significantly different from each other. In your complete answer, remember to include your t-statistic, critical value, and your decision about whether to reject the null hypothesis. For this question, you should assume that different participants received the two different treatments.

b. Now assume that Data Set A depicts the scores of five subjects who received both Treatment 1 and Treatment 2. Calculate a t-test for dependent means to determine whether the means for the two treatments were significantly different. The correlation between the two treatments is +1.00. In your complete answer, remember to include your t-statistic, critical value, and your decision about whether to reject the null hypothesis. For this question, you should assume that the same participants received each of the two treatments.

Data set A:

Treatment 1	Treatment 2
45	60
50	70
55	80
60	90
65	100

Please provide full and detailed answer, and please do not use excel or other programs, rather just answer using the formulas etc.

Thank you very much! :)

A researcher conducted an ANOVA (alpha = .05) between 4 groups (G1, G2, G3, G4), with 11 people in each group. The MSBetween was 5.62 and the MSWithin was 2, leading to an F test statistic of 2.81.

Answer the following:

1) What were the hypotheses in statistical notation (2 points)?

2) What is the critical value (1 point)?

3) Make a decision regarding whether to reject H0 and what that means with regard to the group means (3 points).

4) What specifically do the MSBetween and MSWithin represent when the null hypothesis is true and when the null hypothesis is false (2 points)?

give example for a static mathematical model?

Describe how the researcher should apply the five basic steps in a statistical study. ( Assume that all the people in the poll answered truthfully).

The percentage of workers that drink coffee or tea

a. The population is all workers. The researcher wants to estimate the percentage in this population that do not drink coffee or tea.

B. The population is all workers. The researcher wants to estimate the percentage in this population that drink coffee or tea.

C. The population is all workers that do not drink coffee or tea. The researcher wants to estimate the number in this population that drink coffee or tea.

D. The population is all workers that drink coffee or tea. The researcher wants to estimate the number in this population that drink coffee or tea.

Determine how to apply the second basic step in a statistical study in this situation.

A. The researchers should only gather raw data from workers that drink coffee or tea.

B. the researcher should gather data about drinking coffee or tea from the largest sample of workers from which the researcher can gather data.

C. the researcher should only gather raw data from workers that do not drink coffee or tea

D. the researcher should gather raw data from all the workers about whether or not they drink coffee or tea.

Determine how to apply the third step in the statistical study in this situation:

A. the sample statistic of interest is the number of workers in the sample that do not drink coffee or tea.

B. The sample statistic of interest in the percentage of workers in the sample that do not drink coffee or tea

C. the sample statistic of interest is the percentage of workers in the sample that drink coffee or tea

D. the sample statistic of interest is the number of workers in the sample that drink coffee or tea

Determine how to apply the fourth basic step in the statistical study in this situation.

A. If the researcher followed correct procedures, he or she can be confident that the sample statistics is equal to the percentage of workers in the population that drink coffee or tea

B. the researcher should use the sample statistic as an estimate for the population value of the percentage of workers that drink coffee or tea and then use the methods of statistics to determine how good that estimate is.

C. If the percentage of workers that drink coffee or tea is greater than 50% in the sample, the researcher can be confident that all workers drink coffee or tea

D. The sample statistics provides no useful information to the researcher in this situation

Determine how to apply the fifth basic step in the statistical study in this situation.

A. the researcher should use the methods of the statistics to determine the quality of the estimate of the population parameter and draw conclusions based on this estimate accordingly.

B. the researcher knows that the sample static is equal to the population parameter, so he or she may draw conclusion with complete confidence.

C. there is no way to determine how well the sample statistic estimates the population parameter,

D. the researcher cannot draw any conclusion based on the value of the sample statistic.

According to one survey taken a few years ago, 32% of American households have attempted to reduce their long-distance phone bills by switching long-distance companies. Suppose that business researchers want to test to determine if this figure is still accurate today by taking a new survey of 80 American households who have tried to reduce their long-distance bills. Suppose further that of these 80 households, 22% say they have tried to reduce their bills by switching long-distance companies. Is this result enough evidence to state that a significantly different proportion of American households are trying to reduce long-distance bills by switching companies? Let α = .01.

Suppose 5 of 25 Ford subcompact automobiles require adjustment of some kind. Four subcompacts are selected at random. We are interested in the probability that exactly one will require adjustment. a. Solve the problem assuming that of the 25 subcompacts, the samples are drawn without replacement. b. Solve the problem assuming the sampling is done with replacement c. Assuming the replacement, work the problem using the Poisson distribution.

the shape of the distribution of the time required to get an oil change at a 20​-minute ​oil-change facility is unknown.​ However, records indicate that the mean time is 21.2 minutes​, and the standard deviation is 3.4 minutes.

Complete parts ​(a) through (c).

​(a) To compute probabilities regarding the sample mean using the normal​ model, what size sample would be​ required?

​(b) What is the probability that a random sample of n=45 oil changes results in a sample mean time less than 20 ​minutes?

​(c) Suppose the manager agrees to pay each employee a​ $50 bonus if they meet a certain goal. On a typical​ Saturday, the​ oil-change facility will perform 45 oil changes between 10 A.M. and 12 P.M. Treating this as a random​ sample, there would be a​ 10% chance of the mean​ oil-change time being at or below what​ value? This will be the goal established by the manager.