Cloud seeding has been studied for many decades as a weather modification procedure. The rainfall in acre feet from 20 clouds that were selected at random and seeded with silver nitrate follows: 18.0, 30.7, 19.8, 27.1, 22.3, 18.8, 31.8, 23.4, 21.2, 27.9, 31.9, 27.1, 25.0, 24.7, 26.9, 21.8, 29.2, 34.8, 26.7, 31.6

a) Is there evidence that the mean rainfall from seeded clouds exceeds 25 acre-feet? (1 pt)

b) If the true mean rainfall is 27 acre-feet, what is the probability of the test to indicate that the mean rainfall exceeds 25 acre-feet with a type-I error probability of 0.01? (1 pt)

c) If the true mean rainfall is 27.5 acre-feet, what sample size would be required if you want the test to correctly indicate 90% of the time that the mean rainfall exceeds 25 acre-feet with a type-I error probability of 0.01?

A new operator was recently assigned to a crew of workers who perform a certain job. From the records of the number of units of work completed by each worker each day last month, a sample of size five was randomly selected for each of the two experienced workers and the new worker. At the α = .05 level of significance, does the evidence provide sufficient reason to reject the claim that there is no difference in the amount of work done by the three workers?

(a) Find the test statistic. (Give your answer correct to two decimal places.)


(ii) Find the p-value. (Give your answer bounds exactly.)
_____< p < ____

An experiment was designed to compare the lengths of time that four different drugs provided pain relief after surgery. The results (in hours) follow. Is there enough evidence to reject the null hypothesis that there is no significant difference in the length of pain relief provided by the four drugs at α = .05?

(a) Find the test statistic. (Give your answer correct to two decimal places.)


(ii) Find the p-value. (Give your answer bounds exactly.)
____< p < ____

1. Your brother Eric plays hockey and you attend their game. Eric likes to be the goalkeeper, but it depends on who his coach is that day. Coach Peter prefers Eric to not be goalkeeper and will assign Eric to be a goalkeeper with 0.3 probability. Coach Jared will assign Eric to be a goalkeeper 50% of the time. Coach Jared is the main coach attending 8 out of 10 games. A.) Fill in the probability tree or tree diagram to display this scenario. B.) A food truck near the west coast sells the best tacos. 75% of the time, people will choose the tacos vs something else. The cooks need help calculating the chances of the following situations. What is the chance of selling none of the customers the tacos given there are 5 customers in line? Use 5 decimals. What is the probability of selling the tacos to at least one customer of the 5 in line? Use hand calculations and use 5 decimals.

2. An elementary school employs 20 teachers; 12 are women and 8 are men. Two teachers are selected at random to meet the governor. Is this selection done with or without replacement?

a) What is the chance that both are women?

b) What is the chance that at least one is a women?

c) What is the chance that both are the same gender?

A police department released the numbers of calls for the different days of the week during the month of​ October, as shown in the table to the right. Use a

0.010.01

significance level to test the claim that the different days of the week have the same frequencies of police calls. What is the fundamental error with this​ analysis?

Determine the null and alternative hypotheses.

Upper H 0H0​:

▼

At least one day has a different frequency of calls than the other days.

Police calls occur with all different frequencies on the different days of the week.

Police calls occur with the same frequency on the different days of the week.

At least two days have a different frequency of calls than the other days.

Upper H 1H1​:

▼

Police calls occur with the same frequency on the different days of the week.

Police calls occur with all different frequencies on the different days of the week.

At least two days have a different frequency of calls than the other days.

At least one day has a different frequency of calls than the other days.

Calculate the test​ statistic,

chi squaredχ2.

chi squaredχ2equals=nothing

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

Calculate the​ P-value.

​P-valueequals=nothing

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

What is the conclusion for this hypothesis​ test?

A.

RejectReject

Upper H 0H0.

There is

sufficientsufficient

evidence to warrant rejection of the claim that the different days of the week have the same frequencies of police calls.

B.

Fail to rejectFail to reject

Upper H 0H0.

There is

insufficientinsufficient

evidence to warrant rejection of the claim that the different days of the week have the same frequencies of police calls.

C.

Fail to rejectFail to reject

Upper H 0H0.

There is

sufficientsufficient

evidence to warrant rejection of the claim that the different days of the week have the same frequencies of police calls.

D.

RejectReject

Upper H 0H0.

There is

insufficientinsufficient

evidence to warrant rejection of the claim that the different days of the week have the same frequencies of police calls.

What is the fundamental error with this​ analysis?

A.

Because October has 31​ days, two of the days of the week occur more often than the other days of the week.

B.

Because October has 31​ days, three of the days of the week occur more often than the other days of the week.

C.

Because October has 31​ days, each day of the week occurs the same number of times as the other days of the week.

D.

Because October has 31​ days, one of the days of the week occur more often than the other days of the week.

4. One hundred draws are made at random with replacement form the box [1  3 3  9]

Assume SD_b=3 .

a) How large can the sum be? How small?

b) Find the expected value and the standard error for the sum of draws.

Show them on the normal curve.

b) How likely is the sum to be in the range 370 to 430

c) How likely is the sum to be larger than 500?

6. A quiz has 25  multiple choice questions. Each question has 3 possible answers, one of which is correct.  A correct answer is worth 4 points (a ticket with the value of 4), but a point is taken off for each incorrect answer (a ticket with the value of -1). A student answers all 25 questions by guessing at random.

a) Present the problem with an appropriate box model.

Find the expected value and the standard error for the sum of 25 draws. Interpret this sum in terms of the scores.

b) What is the chance that the student will get a score above 50?

II:  Now replace the tickets with the value of -1 by the tickets with the value of 0.

a) Make a box model.  Find the expected value and the standard error for the sum of 25 draws. Interpret the result.

b) What is the chance that the student will get a score above 50?

3.  A box contains two red balls and three green balls.

Make a box model.

Six draws are made with replacementfrom the box. Find the chance that:

a)   A redball is never drawn.

b)  A green ball appears exactly three times.

Solve for the predicted values of y and the residuals for the following data.

Do not round the intermediate values. (Round your answers to 3 decimal places.)

1. Suppose the National Transportation Safety Board (NTSB) wants to examine the safety of compact cars, midsize cars, and full-size cars. It collects a sample of three for each of the treatments (cars types). Using the data provided below, test whether the mean pressure applied to the driver’s head during a crash test is equal for each types of car. Use α = 5%.

                The average for all can be found as 52.3.

             a). Find SSG.

             b). Find SSE.

             c). Find SST

             d). Find F-value

            e). Find F-critical value from the Table.

            f). Make your decision.

- What is a normal distribution and why is it useful for understanding probabilities and statistics? Provide an example of a normal distribution and explain why it can be categorized as a normal distribution.

- What is the difference between a standard normal distribution and a normal distribution?

- How do we standardize a normal distribution?

- What is a z-score? How do we calculate the z-score for a normal variable?

- How could the standard normal (z) distribution table be used to calculate the probability of:

a) the cumulative area less than a z-score?

b) the cumulative area greater than a z-score?

c) the area between two z-scores?

Directions:  you are required to “Start a New Thread” by Day 3. Initial post should be 200-300 words

There is concern that the Type 2 diabetes drug Avandia raises the risk of having a heart attack. The general population of people with Type 2 diabetes has a 20.2% chance of heart attack within 7 years. In a random sample of 4,485 people with Type 2 diabetes and who used Avandia, 28.9% of these individuals had a heart attack within 7 years. If researchers want to compute the z-test for this data, what assumption should they check?

A) because the sample size is large enough, they dont have to check any assumptions

B)They Need to check both 4485 x .202 and 4485 x (1-.202) are at least 10

Please explain

The quality control department of John Deere measured the length of 100 bolts randomly selected from a specified order. The mean length was found to be 9.75 cm, and the standard deviation was 0.01 cm. if the bolt lengths are normally distributed, find:

a) The percentage of bolts shorter than 9.74 cm

b) The percentage of bolts longer than 9.78 cm

c) The percentage of bolts that meet the length specification of 9.75 +/- 0.02 cm

d) The percentage of bolts that are longer than the nominal length o f9.75 cm

show work

In R, Create a function that replaces the negative values in a numeric matrix with a random integer between 1 and 10. At the same time, it counts the negative values and prints their number. Apply the function to a 4 by 5 matrix of random continuous uniform values ranging from -10 to 10.

A project based on touch therapy is presented at a science fair by a local high school student. In the study, practitioners of touch therapy are blindfolded to see if they can detect a "human energy field (HEF)" without touching patients. The student believes that a practitioner with less years of experience predicts more correct choices to detect HEF. What can be concluded with α = 0.01?

a) What is the appropriate statistic?
---Select--- na Correlation Slope Chi-Square
Compute the statistic selected above:  

b) Compute the appropriate test statistic(s) to make a decision about H₀.
(Hint: Make sure to write down the null and alternative hypotheses to help solve the problem.)
Critical value =  ; Test statistic =  
Decision:  ---Select--- Reject H0 Fail to reject H0

c) Compute the corresponding effect size(s) and indicate magnitude(s).
If not appropriate, input and/or select "na" below.
Effect size =  ;   ---Select--- na trivial effect small effect medium effect large effect

d) Make an interpretation based on the results.

Practitioners with more years of experience predict more HEF correctly.Practitioners with less years of experience predict more HEF correctly.    Practitioners' years of experience does not predict detecting HEF.

Make a scatterplot and include here

Calculate the regression line.