Answer in sentences and be logical!
(a) What does it mean for two events to be disjoint? What does it mean for two events to be independent? Give an example of each [not from parts (b) and (c)!].
(b) Consider a family with two children and define the events
            G₁ = { 1^st child is a girl }
            G₂ = { 2^nd child is a girl }
Using these events, discussion the question: Are independent events always disjoint?
(c) Consider a family with one child and define the events
            B = { child is a boy }
            G = { child is a girl }
Using these events, discussion the question: Are disjoint events always independent?

1. The Ontario Ministry of Transportation is studying the relative safety of compact cars, mid-sized cars, and full size cars. Safety data is collected from a random sample of four cars for each of three car types. Using the data provided below, test whether the mean pressure applied to the driver’s head during a crash test is on average equal for each of the car types. Use a significance level of 1%. Please show all the steps

Use the sample data and confidence level given below to complete parts​ (a) through​ (d).

A drug is used to help prevent blood clots in certain patients. In clinical​ trials, among 4330 patients treated with the​ drug, 121 developed the adverse reaction of nausea. Construct a 99​% confidence interval for the proportion of adverse reactions.

a) Find the best point estimate of the population proportion p.

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

b) Identify the value of the margin of error E.

E = ?

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

c) Construct the confidence interval.

? < p < ?

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

​d) Write a statement that correctly interprets the confidence interval. Choose the correct answer below.

A.One has 99​% confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion.

B.One has 99​% confidence that the sample proportion is equal to the population proportion.

C. 99​% of sample proportions will fall between the lower bound and the upper bound.

D.There is a 99​% chance that the true value of the population proportion will fall between the lower bound and the upper bound.

A statistical analysis is made of the midterm and final scores in a large course, with the following results: Average midterm score = 65, SD = 10, Average final score = 65, SD = 12, r = 0.6 The scatter diagram is football shaped.

a. About what percentage of the class final scores above 70?

b. A student midterm was 75. Predict his final score

c. Suppose the percentile rank of midterm score was 95%, predict his percentile rank on the final score

d. Of those whose midterm score was 70, about what percentage of final scores over 80?

Given the computer output shown following for testing the hypotheses

                                    H_o: (μ₁ - μ₂) = 0

                                    H_a: (μ₁ - μ₂) > 0

            What conclusion would you draw, with α = .10? What assumption(s) did you make in      answering this question?

            Variable: X

Every road has one at some point - construction zones that have much lower speed limits. To see if drivers obey these lower speed limits, a police officer uses a radar gun to measure the speed (in miles per hours, or mph) of a random sample of 10 drivers in a 25 mph construction zone. Here are the data: 27; 33; 32; 21; 30; 30; 29; 25; 27; 34. Is there convincing evidence that at the α=0.01 significance level that the average speed of drivers in this construction zone is greater than the posted speed limit?

The owner of the House of Greens Greenhouse wants to estimate the mean height that her seedlings grow. A sample of 29 plants were chosen and their growth was recorded over a period of a month. It was found that the sample mean was 20.00 cm and the sample standard deviation was 2.25 cm. Given this information, develop a 99.0% confidence interval estimate for the population mean (assuming the best point estimate for the population mean is the sample mean).

In a survey of 520 potential jurors, one study found that 360 were regular watchers of at least one crime-scene forensics television series.

(a) Assuming that it is reasonable to regard this sample of 520 potential jurors as representative of potential jurors in the United States, use the given information to construct a 95% confidence interval for the true proportion of potential jurors who regularly watch at least one crime-scene investigation series.

In 2017, the entire fleet of light‑duty vehicles sold in the United States by each manufacturer must emit an average of no more than 86 milligrams per mile (mg/mi) of nitrogen oxides (NOX) and nonmethane organic gas (NMOG) over the useful life (150,000 miles of driving) of the vehicle. NOX + NMOG emissions over the useful life for one car model vary Normally with mean 82 mg/mi and standard deviation 5 mg/mi.

(a) What is the probability that a single car of this model emits more than 86 mg/mi of NOX + NMOG? (Enter your answer rounded to four decimal places.)

(b) A company has 25 cars of this model in its fleet. What is the probability that the average NOX + NMOG level x¯ of these cars is above 86 mg/mi? (Enter your answer rounded to four decimal places.

Two catalysts are being analyzed to determine how they affect the mean yield of a chemical process. Specifically, catalyst 1 is currently used. Because catalyst 2 is cheaper, it should be adopted, if it does not change the process yield. A test is run in the pilot plant and results in the data shown in the Table below. Both populations are assumed normal.

a) Assuming equal variances, using a hypothesis test at 5% alpha level, show if there is any difference in the mean yields.

b) Assuming unequal variances, using a hypothesis test at 5% alpha level, show if catalyst 2 yields greater mean than catalyst 1.

c) Find a 95% confidence interval for the mean of catalyst 1 minus that of catalyst 2 assuming equal variances.

Question

Runners is a well established company with thousands of employees and they want to estimate the average age of their workers. A sample of 10 employees was taken. Assuming the population has a standard deviation of 8, we want to find a 90% confidence interval for the population mean.

If the mean of the sample is 31.5, what is the confidence interval estimate?

A population standard deviation is estimated te be 11 . we want to estimate the population mean within 0.5 with 90 percent of level of confidence . what sample size is required ?

4. A study of the effect of television commercials on 12-year-old children measured their attention span, in seconds. The commercials were for clothes, food, and toys.

  Click here for the Excel Data File

1. Complete the ANOVA table. Use 0.05 significance level. (Round the SS and MS values to 1 decimal place and F value to 2 decimal places. Leave no cells blank — be certain to enter "0" wherever required. Round the df values to nearest whole number.)
2. Find the values of mean and standard deviation. (Round the mean and standard deviation values to 3 decimal places.)
3. Is there a difference in the mean attention span of the children for the various commercials?
4. Are there significant differences between pairs of means?

A start-up company has 2000 investors, that company loses investors at a rate of 10 per year. Every time the company loses an investor, the company gets a loss of $200,000. For every investor that remains the company makes a profit of $2,000. Let F be the total earnings the company makes in a year, and X be the number of investors the company loses.

1)Write a function that calculates yearly earnings F as a function of X

2)Find P(F < 0), the probability that earnings are negative

3)E[F]

4)What is the probability that the company loses exactly 5 investors in a given year, given that they have not lost any investors in the first half of the year

How do multiple comparison techniques differ when we do two-way ANOVA as compared to one-way ANOVA?

Construct a confidence interval for p1−p2 at the given level of confidence. x1= 396​, n1= 503​, x2= 424​, n2= 587​, 95​% confidence

The researchers are __?__​% confident the difference between the two population​ proportions,p1−p2​, is between __?__and __?__.

​(Use ascending order. Type an integer or decimal rounded to three decimal places as​ needed.)