An instructor who taught two sections of engineering statistics last term, the first with 25 students and the second with 30, decided to assign a term project. After all projects had been turned in, the instructor randomly ordered them before grading. Consider the first 15 graded projects.

(a) What is the probability that exactly 13 of these are from the second section? (Round your answer to four decimal places.)

(b) What is the probability that exactly 9 of these are from the first section? (Round your answer to four decimal places.)

(c) What is the probability that at all 15 of these are from the same section? (Round your answer to six decimal places.)

If you could please explain how to do it out on a calculator that would be much appreciated as the exam will ask us to solve this problem using a TI 84 plus CE.

Given the following data of temperature (x) and the number of times a cricket chirps in a second (y), run regression analysis and state the regression equation as long as there is a statistically significant linear relationship between the variables.

A friend who lives in Los Angeles makes frequent consulting trips to Washington, D.C.; 50% of the time she travels on airline #1, 20% of the time on airline #2, and the remaining 30%of the time on airline #3. For airline #1, flights are late into D.C. 15% of the time and late into L.A. 10% of the time. For airline #2, these percentages are 40% and 30%, whereas for airline #3 the percentages are 35% and 20%. If we learn that on a particular trip she arrived late at exactly one of the two destinations, what are the posterior probabilities of having flown on airlines #1, #2, and #3? Assume that the chance of a late arrival in L.A. is unaffected by what happens on the flight to D.C. [Hint: From the tip of each first-generation branch on a tree diagram, draw three second-generation branches labeled, respectively, 0 late, 1 late, and 2 late.] (Round your answers to four decimal places.)

Market research has indicated that customers are likely to bypass Roma tomatoes that weigh less than

70 grams. A produce company produces Roma tomatoes that average 78.0 grams with a standard

deviation of 5.2 grams.

i) Assuming that the normal distribution is a reasonable model for the weights of these

tomatoes, what proportion of Roma tomatoes are currently undersize (less than 70g)?

ii) How much must a Roma tomato weigh to be among the heaviest 20%?

iii) The aim of the current research is to reduce the proportion of undersized tomatoes

to no more than 2%. One way of reducing this proportion is to reduce the standard deviation.

If the average size of the tomatoes remains 78.0 grams, what must the target standard deviation

be to achieve the 2% goal?

iv) The company claims that the goal of 2% undersized tomatoes is reached. To test this,

a random sample of 20 tomatoes is taken. What is the distribution of the number of undersized

tomatoes in this sample if the company's claim is true? Explain your reasoning.

v) Suppose there were 3 undersized tomatoes in the random sample of 20. What is the

probability of getting at least 3 undersized tomatoes in a random sample of 20 if the company's

claim is true? Do you believe the company's claim? Why or why not?

Consider an earnings function with the dependent variable y monthly usual earnings and as independent variables years of education x1, gender x2 coded as 1 if female and 0 if male, and work experience in years x3. We are interested in the partial effect of years of education on earnings. We consider the following possible relations (that are assumed to be exact) y =β0 + β1x1 + β2x2 + β3x3 (1) y =β0 + β1x1 + β2x2 + β3x3 + β4x 2 1 (2) y =β0 + β1x1 + β2x2 + β3x3 + β4x1x2 (3) We are interested in the partial, i.e. ceteris paribus, effect of x1 on earnings y. (i) Use partial differentiation to find the partial effect in the three specifications above. (ii) For which specifications are the partial effects constant, i.e. independent of the level of x1, x2, x3? If not constant how does the partial effect change with x1, x2, x3? (iii) If we have data that allow us to estimate the regression coefficients, how would you report the partial effects if they are not constant and you still want to report a single number? (iv) Can you use partial differentiation to find the partial effect of x2? Why (not)? (v) Often work experience is not directly observed, but measured as AGE YEARS OF EDUCATION - 6. Does this change your answers to (i) and (ii)?

Could u pls explain step by step?

Thank you

Thank

What does it mean to take a sampling of a population? Why do scientists use samplings?

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Self-Test Tutorial

Consider a sample with a mean of 40 and a standard deviation of 5. Use Chebyshev's theorem to determine the percentage of the data within each of the following ranges (to the nearest whole number).

1. 30 to 50, at least _____ %
   
2. 25 to 55, at least _____ %
   
3. 31 to 49, at least _____ %
   
4. 28 to 52, at least _____ %
   
5. 22 to 58, at least _____ %

Suppose the people living in a city have a mean score of 41 and a standard deviation of 8 on a measure of concern about the environment. Assume that these concern scores are normally distributed. Using the ​50% minus −​34% minus −​14% ​figures, approximately what percentage of people have a score​ (a) above 41​, ​(b) above 49​, ​(c) above 25​, ​(d) above 33​, ​(e) below 41​, ​(f) below 49​, ​(g) below 25​, and​ (h) below 33​?

The accompanying data represent the pulse rates​ (beats per​ minute) of nine students. Treat the nine students as a population. Compute the​ z-scores for all the students. Compute the mean and standard deviation of these​ z-scores.

Student   Pulse
Student 1   77
Student 2   60
Student 3   60
Student 4   80
Student 5   72
Student 6   80
Student 7   80
Student 8   68
Student 9   73

Compute the mean of these​ z-scores.

The mean of the​ z-scores is

​(Round to the nearest tenth as​ needed.)

Compute the standard deviation of these​ z-scores.

The standard deviation of the​ z-scores is
(Round to the nearest tenth as​ needed.)

3. Recently, ESPN reported that the average salary of an NFL place-kicker is $1.9 million, while the average salary for an NFL running back is only $1.7 million. This statistic was cited as evidence that, in the current NFL, running backs are considered less valuable than place-kickers. The claim being made based on this statistic is misleading. In what way?   (Hint: Teams have 1 place-kicker and, usually, 5 or 6 running backs, one of whom is their lead back.)

Compute in excel

A college admission officer for an MBA program determines that historically candidates have undergraduate grade averages that are normally distributed with standard deviation of .45. A random sample of 25 applications from the current year yields a sample mean grade point average of 2.90. (i) Find a 95% confidence interval for the population mean, μ. (Round the boundaries to 2 decimal places.) (ii) Based on the same sample results, a statistician computes a confidence interval for the population mean as 2.81< μ < 2.99. Find the α for this interval and the probability content (1- α) as well. (Round to 4 digits.) (Note: the correct α is a higher number than traditional α used; so don’t worry if your number “looks” wrong!) Hint: first calculate α/2 using either the lower bound (2.81) or upper bound (2.99); then calculate α. Finally, calculate the probability content of the interval, which is (1- α). And make sure you use the standard error, not the standard deviation, to calculate α/2.

Consider the following competing hypotheses and accompanying sample data. (You may find it useful to reference the appropriate table: z table or t table)  

H₀: μ₁ – μ₂ = 5
H_A: μ₁ – μ₂ ≠ 5

Assume that the populations are normally distributed with equal variances.

a-1. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)

a-2. Find the p-value.

• p-value < 0.01

• 0.01 ≤ p-value < 0.02

• 0.02 ≤ p-value < 0.05

• 0.05 ≤ p-value < 0.10

• p-value ≥ 0.10

b. At the 5% significance level, can you conclude that the difference between the two means differs from 5?

Consider the following data drawn independently from normally distributed populations: (You may find it useful to reference the appropriate table: z table or t table)

a. Construct the 95% confidence interval for the difference between the population means. Assume the population variances are unknown but equal. (Round all intermediate calculations to at least 4 decimal places and final answers to 2 decimal places.)
  

b. Specify the competing hypotheses in order to determine whether or not the population means differ.
  

• H₀: μ₁ − μ₂ = 0; H_A: μ₁ − μ₂ ≠ 0

• H₀: μ₁ − μ₂ ≥ 0; H_A: μ₁ − μ₂ < 0

• H₀: μ₁ − μ₂ ≤ 0; H_A: μ₁ − μ₂ > 0

c. Using the confidence interval from part a, can you reject the null hypothesis?
  

• Yes, since the confidence interval includes the hypothesized value of 0.

• No, since the confidence interval includes the hypothesized value of 0.

• Yes, since the confidence interval does not include the hypothesized value of 0.

• No, since the confidence interval does not include the hypothesized value of 0.

d. Interpret the results at αα = 0.05.

• We conclude that population mean 1 is greater than population mean 2.

• We cannot conclude that population mean 1 is greater than population mean 2.

• We conclude that the population means differ.

• We cannot conclude that the population means differ.