Each of the following statements contains an error. Describe each error and explain why the statement is wrong.

(a) If the residuals are all negative, this implies that there is a negative relationship between the response variable and the explanatory variable.

(b) A strong negative relationship does not imply that there is an association between the explanatory variable and the response variable.

(c) A lurking variable is always something that can be measured.

The average length of a maternity stay in a U.S. hospital is said to be 2.2 days with a standard deviation of 0.9 days. We randomly survey 80 women who recently bore children in a U.S. hospital.

B)Give the distribution of

X.

(Round your standard deviation to two decimal places.)

C)Give the distribution of ΣX. (Round your standard deviation to two decimal places.)

A study is conducted to survey (in thousands) of earned degrees in the United States in a recent year. The table is given below.

a) If one person is randomly selected, find the probability that this person is a female.      

  b)  If one person is randomly selected, find the probability that this person has a bachelor degree and is a male.   

  c)   If one person is randomly selected, find the probability that this person has an AA degree.  

d) If one person is randomly selected, find the probability that this person is a female, giventhat the person received an AA degree.

e) If one person is randomly selected, find the probability that this person has a master degree or is a female.

f) Are the events “female” and “AA degree” independent? Why or why not? Use the answers from a) and d) above to explain this.

g) If two people are randomly selected, find the probability that these two people are males.

The weights​ (in pounds) of 6 vehicles and the variability of their braking distances​ (in feet) when stopping on a dry surface are shown in the table. Can you conclude that there is a significant linear correlation between vehicle weight and variability in braking distance on a dry​ surface? use alpha=0.05 weight,X 5960, 5330, 6500, 5100, 5890, 4800 variability in 1.79, 1.95, 1.89, 1.55, 1.65, 1.50 breaking distance,Y set up the hypothesis for the test H o: P=0 H a: P does not equal 0 Identify the critical​ value(s).

Select the correct choice below and fill in any answer boxes within your choice. ​(Round to three decimal places as​ needed.) Answer A or B A. negative t o = ____ and positive t o = ____ B. the critical value is ____. choose one and fill in blank with value ____. The Correct Answer was A. negative t o = -2.766 and positive t o = 2.766 You gave me as the Expert Answer of B. The critical value is .811 which was Incorrect.

My New Question is... Calculate the test statistic. t= ____ (Round to three decimal places as needed.) The answer was t= 1.564 which was correct <- this question is done the new one is under

New Question... There (Is/Is Not) enough evidence at the 5​% level of significance to conclude that there (Is/Is Not) a significant linear correlation between vehicle weight and variability in braking distance on a dry surface. Choose 1 for each Is or Is Not. This is a 2 part question fill in the blanks with Is or Is Not.

An organization monitors many aspects of elementary and secondary education nationwide. Their 2000 numbers are often used as a baseline to assess changes. In 2000 48 % of students had not been absent from school even once during the previous month. In the 2004 ​survey, responses from 6827 randomly selected students showed that this figure had slipped to 47 %. Officials would note any change in the rate of student attendance. Answer the questions below.

​(a) Write appropriate hypotheses.

Upper H 0 : The percentage of students in 2004 with perfect attendance the previous month ▼ is greater than 48%. is less than 48%. is different from 48%. is equal to 48%.

Upper H Subscript Upper A Baseline : The percentage of students in 2004 with perfect attendance the previous month ▼ is greater than 48%. is equal to 48%. is less than 48%. is different from 48%.

(b) Check the necessary assumptions.

The independence condition is ▼ satisfied. not satisfied. The randomization condition is ▼ not satisfied. satisfied. The​ 10% condition is ▼ satisfied. not satisfied. The​ success/failure condition is ▼ not satisfied. satisfied. ​

(c) Perform the test and find the​ P-value. ​P-value equals ________ ​(Round to three decimal places as​ needed.) ​

(d) State your conclusion. Assume a=0.05.

A. We fail to reject the null hypothesis. There is sufficient evidence to suggest that the percentage of students with perfect attendance in the previous month has changed.

B. We can reject the null hypothesis. There is sufficient evidence to suggest that the percentage of students with perfect attendance in the previous month has changed.

C. We fail to reject the null hypothesis. There is not sufficient evidence to suggest that the percentage of students with perfect attendance in the previous month has changed.

We anticipate that deadly two vehicle motorcycle accidents occur at the same frequency on all seven days of the week. However, is this true? The table shows the number of two-vehicle crashes including a motorbike and a passenger vehicle, with day of week, in a random sample of 1,792 accidents

A.What is the null and the alternative hypothesis.

B.Find the χ2 statistic and the degrees of freedom.

C.Use the critical value way to find the P-value with a significance level of α=0.05

D.What is the conclusion

Recall that Benford's Law claims that numbers chosen from very large data files tend to have "1" as the first nonzero digit disproportionately often. In fact, research has shown that if you randomly draw a number from a very large data file, the probability of getting a number with "1" as the leading digit is about 0.301. Now suppose you are the auditor for a very large corporation. The revenue file contains millions of numbers in a large computer data bank. You draw a random sample of n = 227 numbers from this file and r = 86 have a first nonzero digit of 1. Let p represent the population proportion of all numbers in the computer file that have a leading digit of 1.

(i) Test the claim that p is more than 0.301. Use α = 0.10.

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: p > 0.301; H₁: p = 0.301H₀: p = 0.301; H₁: p > 0.301    H₀: p = 0.301; H₁: p < 0.301H₀: p = 0.301; H₁: p ≠ 0.301

(b) What sampling distribution will you use?

The Student's t, since np < 5 and nq < 5.The standard normal, since np < 5 and nq < 5.    The standard normal, since np > 5 and nq > 5.The Student's t, since np > 5 and nq > 5.

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


(c) Find the P-value of the test statistic. (Round your answer to four decimal places.)


Sketch the sampling distribution and show the area corresponding to the P-value.

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?

At the α = 0.10 level, we reject the null hypothesis and conclude the data are statistically significant.At the α = 0.10 level, we reject the null hypothesis and conclude the data are not statistically significant.    At the α = 0.10 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the α = 0.10 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(e) Interpret your conclusion in the context of the application.

There is sufficient evidence at the 0.10 level to conclude that the true proportion of numbers with a leading 1 in the revenue file is greater than 0.301.There is insufficient evidence at the 0.10 level to conclude that the true proportion of numbers with a leading 1 in the revenue file is greater than 0.301.    

(ii) If p is in fact larger than 0.301, it would seem there are too many numbers in the file with leading 1's. Could this indicate that the books have been "cooked" by artificially lowering numbers in the file? Comment from the point of view of the Internal Revenue Service. Comment from the perspective of the Federal Bureau of Investigation as it looks for "profit skimming" by unscrupulous employees.

No. There seems to be too many entries with a leading digit 1.Yes. There does not seem to be too many entries with a leading digit 1.    No. There does not seem to be too many entries with a leading digit 1.Yes. There seems to be too many entries with a leading digit 1.

(iii) Comment on the following statement: If we reject the null hypothesis at level of significance α , we have not proved H₀ to be false. We can say that the probability is α that we made a mistake in rejecting H_o. Based on the outcome of the test, would you recommend further investigation before accusing the company of fraud?

We have proved H₀ to be false. Because our data lead us to reject the null hypothesis, more investigation is not merited.We have not proved H₀ to be false. Because our data lead us to reject the null hypothesis, more investigation is not merited.    We have not proved H₀ to be false. Because our data lead us to reject the null hypothesis, more investigation is merited.We have not proved H₀ to be false. Because our data lead us to accept the null hypothesis, more investigation is not merited.

Nationally, about 11% of the total U.S. wheat crop is destroyed each year by hail.† An insurance company is studying wheat hail damage claims in a county in Colorado. A random sample of 16 claims in the county reported the percentage of their wheat lost to hail.

The sample mean is x = 12.2%. Let x be a random variable that represents the percentage of wheat crop in that county lost to hail. Assume that x has a normal distribution and σ = 5.0%. Do these data indicate that the percentage of wheat crop lost to hail in that county is different (either way) from the national mean of 11%? Use α = 0.01.

(a) What is the level of significance?


State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test?

H₀: μ = 11%; H₁: μ ≠ 11%; two-tailedH₀: μ = 11%; H₁: μ < 11%; left-tailed    H₀: μ ≠ 11%; H₁: μ = 11%; two-tailedH₀: μ = 11%; H₁: μ > 11%; right-tailed

(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.

The standard normal, since we assume that x has a normal distribution with known σ.The Student's t, since we assume that x has a normal distribution with known σ.    The standard normal, since we assume that x has a normal distribution with unknown σ.The Student's t, since n is large with unknown σ.

Compute the z value of the sample test statistic. (Round your answer to two decimal places.)


(c) Find (or estimate) the P-value. (Round your answer to four decimal places.)


Sketch the sampling distribution and show the area corresponding to the P-value.

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?

At the α = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.At the α = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.    At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(e) State your conclusion in the context of the application.

There is sufficient evidence at the 0.01 level to conclude that the average hail damage to wheat crops in the county in Colorado differs from the national average.There is insufficient evidence at the 0.01 level to conclude that the average hail damage to wheat crops in the county in Colorado differs from the national average.    

The bacterial strain Acinetobacter has been tested for its adhesion properties. A sample of five measurements gave readings of 2.69, 5.76, 2.67, 1.62 and 4.12 dyne-cm2. Assume that the standard deviation is known to be 0.66 dyne-cm2 and that the scientists are interested in high adhesion (at least 2.5 dyne-cm2).
a) Should the alternative hypothesis be one-sided or two-sided? (5 points)
b) Test the hypothesis that the mean adhesion is 2.5 dyne-cm^2.

Please answer by working it out by hand. Thankyou!

You have 3 coins that look identical, but one is not a fair coin. The probability the unfair coin show heads when tossed is 3/4, the other two coins are fair and have probability 1/2 of showing heads when tossed.

You pick one of three coins uniformly at random and toss it n times, (where n is an arbitrary fixed positive integer).

Let Y be the number of times the coin shows heads. Let X be the probability the coin you choose shows heads when flipped. (Note that X is a random variable because you’re randomly choosing a coin).

a) What is the pmf of X?

b) For each x that the random variable X can equal, give the conditional distribution of Y given X = x.

c) Determine the unconditional distribution of Y .

d) Compute the expectation of Y

1. (Memoryless property) [10]

Consider a discrete random variable X ∈ N (X ∈ N is a convention to represent that the range of X is N). It is memoryless if

Pr{X > n + m|X > m} = Pr{X > n}, ∀m,n ∈{0,1,...}.

a) Let X ∼ G(p), 0 < p ≤ 1. Show that X is memoryless. [2]

b) Show that if a discrete positive integer-valued random variable X is memoryless, it must be a geometric random variable, that is, their PMFs are identical. [3]

Now, let us consider a continuous positive random variable X, that is, its distribution function FX(t) = 0 when t < 0. It is memoryless if

Pr{X > s + t|X > s} = Pr{X > t}, ∀s,t ∈ [0,∞).

c) Let X ∼ Exp(λ), λ > 0. Show that X is memoryless. [2]

d) Show that if a continuous positive random variable X is memoryless, it must be an exponential random variable, that is, their distribution functions are identical. [3]

Interpretation: Think of X as the amount of time you wait for a bus. X, the waiting time, being memoryless simply means that no matter how long you have waited, under that condition, the probability you need to further wait for more than a certain amount of time remains the same.

1.) Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 250 feet and a standard deviation of 50 feet. We randomly sample 49 fly balls. Using Excel and the functions show me how you got your answer

1. If¯¯¯¯¯XX¯ = average distance in feet for 49 fly balls, then¯¯¯¯¯XX¯ ~ _______(_______,_______)
2. What is the probability that the 49 balls traveled an average of less than 240 feet? Sketch the graph. Scale the horizontal axis for¯¯¯¯¯XX¯. Shade the region corresponding to the probability. Find the probability. using excel functions
3. Find the 80^th percentile of the distribution of the average of 49 fly balls. using excel functions

2.) Suppose that a category of world-class runners are known to run a marathon (26 miles) in an average of 145 minutes with a standard deviation of 14 minutes. Consider 49 of the races. Let¯¯¯¯¯XX¯ the average of the 49 races. Using Excel and the excel functions for the following questions. Show me how you got your answer

1. ¯¯¯¯¯XX¯ ~ _____(_____,_____)
2. Find the probability that the runner will average between 142 and 146 minutes in these 49 marathons. using excel functions
3. Find the 80^th percentile for the average of these 49 marathons. using excel functions
4. Find the median of the average running times. using excel functions

The following sample observations were randomly selected. (Do not round the intermediate values. Negative amount should be indicated by a minus sign. Round your answers to 3 decimal places.)

X: 4 4 3 6 10

Y: 5 2 6 7 7

Determine the 0.95 confidence interval for the mean predicted when x = 5.

Determine the 0.95 prediction interval for an individual predicted when x = 5.

1.) In 1940 the average size of a U.S. farm was 174 acres. Let’s say that the standard deviation was 55 acres. Suppose we randomly survey 38 farmers from 1940. Using excel and excel functions show me how you got your answer

1. In words, Χ = _____________
2. In words,¯¯¯¯¯XX¯ = _____________
3. ¯¯¯¯¯XX¯~ _____(_____,_____)
4. The IQR for¯¯¯¯¯XX¯ is from _______ acres to _______ acres. excel functions

2.) The percent of fat calories that a person in America consumes each day is normally distributed with a mean of about 36 and a standard deviation of about ten. Suppose that 16 individuals are randomly chosen. Let¯¯¯¯¯XX¯ = average percent of fat calories. Using Excel and excel functions, show me how you got your answer.

1. ¯¯¯¯¯XX¯ ~ ______(______, ______)
2. For the group of 16, find the probability that the average percent of fat calories consumed is more than five. Graph the situation and shade in the area to be determined. excel function
3. Find the first quartile for the average percent of fat calories. excel function

A national organization which promotes good local government management (ICMA) is interested in factors which may predict if a local government has actual ‘e-government’ transactions on their website. One of these is whether the local government is city manager or mayor/council.

a)Provide null and alternative hypothesis in formal terms and layperson’s terms for the chi-square two sample test. Remember to apply Yates if necessary.

b Do math and reject/accept the null at a = .05.

c)Explain the results in layperson’s terms.

d Explain in layperson’s terms the column percentage for the cell ‘has transactions/mayor-council.’