This question involves coding in RStudio Problem 3 (Verzani problem 2.22):

Write a function to compute the average distance from the mean for some data vector.

Perform these hypothesis tests. Show the formulas for the test statistics and what numbers go into them. Clearly show your decision, write it in words, and be sure to write out your null and alternative hypotheses. In a study of 40 heterosexual couples, 28 of the 40 couples the male said “I love you” first. The researchers were interested in learning whether these data provided evidence that in significantly more than 50% of these couples the male says “I love you” first.

During the first 13 weeks of the television season, the Saturday evening 8:00 P.M. to 9:00 P.M. audience proportions were recorded as ABC 29%, CBS 27%, NBC 24%, and independents 20%. A sample of 300 homes two weeks after a Saturday night schedule revision yielded the following viewing audience data: ABC 92 homes, CBS 64 homes, NBC 86 homes, and independents 58 homes. Test with alpha=.05 to determine whether the viewing audience proportions changed. Round your answers to two decimal places.

what is the Test Statistic?

The grades of a group of 1000 students in an exam are normally distributed with a mean of 70 and a standard deviation of 10. A student is randomly selected from the group. Find the probability that;

a. Their grade is greater than 80

b. Their grade is less than 50

c. That their grade is between 50 and 80

d. Approximately, how many students have grade greater than 80% and how many have less than 50%

Please elaborate on the differences and the relationships between Brownian motion, Wiener process and Levy process, and also the characteristics of each.

Thank you so much!

A systems analyst tests a new algorithm designed to work faster than the currently-used algorithm. Each algorithm is applied to a group of 60 sample problems. The new algorithm completes the sample problems with a mean time of 22.16 hours. The current algorithm completes the sample problems with a mean time of 24.18 hours. Assume the population standard deviation for the new algorithm is 5.572 hours, while the current algorithm has a population standard deviation of 4.365 hours. Conduct a hypothesis test at the 0.05 level of significance of the claim that the new algorithm has a lower mean completion time than the current algorithm. Let μ1 be the true mean completion time for the new algorithm and μ2 be the true mean completion time for the current algorithm.

Step 1 of 5: State the null and alternative hypotheses for the test.

Step 2 of 5: Compute the value of the test statistic. Round your answer to two decimal places.

Step 3 of 5: Find the p-value associated with the test statistic. Round your answer to four decimal places.

Step 4 of 5: Make the decision for the hypothesis test.

Step 5 of 5: State the conclusion of the hypothesis test.

The margin of error for a multiple comparisons procedure was determined to be 10.5 units. The sample means for the problem were: A: 47.3 B: 22.5 C: 19.5 D: 38.6. Which of the following statements is INCORRECT?

A manufacturer of colored candies states that 13​% of the candies in a bag should be​ brown, 14​% ​yellow, 13​% ​red, 24​% ​blue, 20​% ​orange, and 16​% green. A student randomly selected a bag of colored candies. He counted the number of candies of each color and obtained the results shown in the table. Test whether the bag of colored candies follows the distribution stated above at the a=0.05 level of significance.

What is the P-value of the test? (round to three decimal places as needed)

2. If the mean of a distribution is 100 with a standard deviation of 10, what raw score is associated with a z-score of +2.003.

3. Using the z-score formula, if you have a distribution with a mean of 50 and a standard deviation of 5, what z-score is associated with a raw score of X=43.5?

4. Using the z-score formula, if you have a distribution with a mean of 50 and a standard deviation of 5, what z-score is associated with a raw score of X=53.1

A math professor claims that the standard deviation of IQ scores of the students majoring in mathematics is different from 15, where 15 is the standard deviation of IQ scores for the general population. To test his claim, 10 students were surveyed and their IQ scores were recorded. 120, 110, 113, 123, 119, 160, 220, 119, 110, 140 Test the professor’s claim using a 0.01 level of significance.

Draw one card with replacement from a well-shuffled standard poker deck until you draw a spade. Find the probability of each of the following:

a. You draw only once.

b. You draw at least once.

c. You draw at least twice.

d. You draw at least three times, but no more than five times.

The mean finish time for a yearly amateur auto race was 187.22 minutes with a standard deviation of 0.377 minute. The winning​ car, driven by Todd. Todd​, finished in 186.63 minutes. The previous​ year's race had a mean finishing time of 110.4 with a standard deviation of 0.112 minute. The winning car that​ year, driven by Karen​, finished in 110.19 minutes. Find their respective​ z-scores. Who had the more convincing​ victory?

The average number of people in a family that received welfare for various years is given below.

y=88.721+ -0.043x

part d.

Find the estimated welfare family size in 1970. (Use your equation from part (b). Round your answer to one decimal place.) _______ people.

Find the estimated welfare family size in 1989. (Use your equation from part (b). Round your answer to one decimal place.)
_______  people.

Use the two points in part (d) to plot the least squares line. (Upload your file below.)

QUESTION 9 A nutritionist claims that children under the age of 10 years are consuming more than the U.S. Food and Drug Administration’s recommended daily allowance of sodium, which is 2400 mg. To test this claim, she obtains a random sample of 75 children under the age of 10 and measures their daily consumption of sodium. This sample has a mean of 2610 mg and leads to a p -value of .124. Claim: The mean level of sodium consumption for children under 10 years of age is more than 2400 mg. Noting that the p -value of .124 is > equation = .05, w hat would be the correct response to this claim?

There is not enough information to make a decision.

The evidence is not strong enough to prove the nutrionist's claim, therefore, the claim is wrong and the mean sodium level is less than 2400 mg.

The evidence is not strong enough to support the nutriontist's claim that the mean sodium level is more than 2400 mg, but this does not mean that the claim is not true.

There is strong evidence to support the nutritionist's claim the the mean sodium level is more than 2400 mg.

Dottie's Tax Service specializes in federal tax returns for professional clients, such as physicians, dentists, accountants, and lawyers. A recent audit by the IRS of the returns she prepared indicated that an error was made on 10% of the returns she prepared last year. Assuming this rate continues into this year and she prepares 62 returns, what is the probability that she makes errors on:

a) More than 6 returns?

b) At least 6 returns?

c) Exactly 6 returns?