The null and alternate hypotheses are: H0: μ1 ≤ μ2 H1: μ1 > μ2 A random sample of 23 items from the first population showed a mean of 107 and a standard deviation of 12. A sample of 15 items for the second population showed a mean of 102 and a standard deviation of 5. Use the 0.025 significant level. Find the degrees of freedom for unequal variance test. (Round down your answer to the nearest whole number.) State the decision rule for 0.025 significance level. (Round your answer to 3 decimal places.) Compute the value of the test statistic. (Round your answer to 3 decimal places.) What is your decision regarding the null hypothesis? Use the 0.03 significance level.

4. To study whether movie ratings and release season influence the box office earnings, you gather data on 70 recent movies. You characterize each movie’s rating (G, PG, PG-13, R, or NC-17) and release season (summer or not summer).
   1. Complete the ANOVA table below by filling in the shaded boxes
   2. Find the appropriate critical value(s) [?=0.05]
   3. Does box office revenue significantly vary with rating, release season, or their interaction? Clearly answer for each

   4. 	SS	df	MS	F
      Rating	455
      Season	192.5
      Interaction	140

Consider the following game: Three cards are labeled $1, $4, and $7. A player pays a $9 entry fee, selects 2 cards at random without replacement, and then receives the sum of the winnings indicated on the 2 cards.

a) Calculate the expected value and standard deviation of the random variable "net winnings" (that is, winnings minus a $9 entry fee)

b) Suppose a 4th card, labelled k, is added to the game but the player still selects two cards without replacement. What is the value of k which makes the game fair (i.e makes expected net winnings = $0)

1. Calculate the test statistic to compare the variance in poverty rates for rural counties to that of urban cities in 2016.

2. Calculate the p-value of the test statistic to compare the variance in poverty rates for rural counties to that of urban counties in 2016.

These are two questions I have for my homework, I have an excel sheet to work with and I just need to know the operations to derive these calculations. Also, is the F-Statistic the test statistic?

To study the effectiveness of possible treatments for insomnia, a sleep researcher
conducted a study with 12 participants. Four participants were instructed to count
sheep (the Sheep Condition), four were told to concentrate on their breathing (the
Breathing Condition), and four were not given any special instructions. Over the next
few days, measures were taken how long it took each participant to fall asleep. The
average times for the participants in the Sheep Condition were 14, 28, 27, and 31; for
those in the Breathing Condition, 25, 22, 17, and 14; and for those in the control
condition, 45, 33, 30, and 41. Do these results suggest that the different techniques have
different effects? Answer the question by conducting a hypothesis test at the 0.05
significant level.
Use the five steps of hypothesis testing and demonstrate your calculations.

Please demonstrate all calculations in detail in your answers including how you found the standard deviations. Thanks.

Suppose you are rolling two independent fair dice. You may have one of the following outcomes

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

(4,1) (4,2) (4,2) (4,4) (4,5)  (4,6)

(5,1) (5,2) (5,3) (5,4) (5,5)  (5,6)

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

Now define a random variable Y = the absolute value of the difference of the two numbers
a. Complete the following pmf of Y with necessary calculations and reasoning.

b. Find the mgf of Y

c. Now further consider another random variable X = the sum of the two numbers. Do you think X and Y are independent? Briefly explain your reasons

A particular meat-processing plant slaughters steers and cuts and wraps the beef for its customers. Suppose a complaint has been filed with the Food and Drug Administration (FDA) against the processing plant. The complaint alleges that the consumer does not get all the beef from the steer he purchases. In particular, one consumer purchased a cut and wrapped beef. To settle the complaint, the FDA collected data on the live weights and dressed weights of nine steers processed by a reputable meat processing plant (not the firm in question). The results are listed in the table.

a. Fit the model E(y)= β₀ + β₁x to the data

b. Construct a 95% prediction interval for the dressed weight y of a 300-pound steer.

c. Would you recommend that the FDA use the interval obtained in part b to determine whether the dressed weight of 150 pounds is a reasonable amount to receive from a 300-pound steer? Explain.

A researcher claims that the mean age of the residents of a small town is more than 32 years. The ages (in years) of a random sample of 36 residents are listed below. At α=0.10, α = 0.10 , alpha equals , 0.10 , comma is there enough evidence to support the researcher's claim? Assume the population standard deviation is 9 years. 41,33,47,31,26,39,19,25,23,31,39,36,41,28,33,41,44,40,30,29,46,42,53,21,29,43,46,39,35,33,42,35,43,35,24,21

Crossett Trucking Company claims that the mean weight of its delivery trucks when they are fully loaded is 5,850 pounds and the standard deviation is 280 pounds. Assume that the population follows the normal distribution. Fifty trucks are randomly selected and weighed.

Within what limits will 95 percent of the sample means occur?

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Question: Find the regression​ equation, letting the first variable be the predictor​ (x) variable. Using t...

Find the regression​ equation, letting the first variable be the predictor​ (x) variable. Using the listed​ actress/actor ages in various​ years, find the best predicted age of the Best Actor winner given that the age of the Best Actress winner that year is 27 years. Is the result within 5 years of the actual Best Actor​ winner, whose age was 45 ​years?

Best Actress: 27, 31, 29, 59, 34, 32, 44, 28, 65, 21, 45, 54

Best Actor: 45, 39, 40, 43, 52, 50, 59, 52, 41, 56, 44, 33

a. Find the equation of the regression line.

b. The best predicted age of the best actor winner given that the age of the best actress winner that is 27 years is ___years old.

Free will is an important concept to individuals and societies. In the context of cognitive neuroscience, mounting evidence suggests that free will is an illusion, constructed by processes in the brain, similar to visual illusions. Recent research has demonstrated that people who believe in free will tend to also believe in the paranormal (Mogi, 2014). A psychologist at Arizona State University (ASU) wanted to replicate this study with students in the psychology major. Following the procedure of Mogi (2014), an anonymous survey was sent to students with a call to participate in a “study of free will.” There was no mention of paranormal beliefs at this stage. One thousand and thirty-eight (1038) students completed the following survey. First, subjects were asked a series of questions regarding their belief in free will. After the free will questions, subjects were asked a series of questions regarding their belief in the paranormal. Care was taken so that the questions related to the paranormal was not phrased in a way that suggested a correlation between free will and the paranormal. Below are the findings:

1. (Test of Independence) The researcher now wants to look at just the psychology students at ASU. Does this data suggest a significant relationship between belief in free will and belief in the paranormal amongst the budding psychologists at ASU?
   
   1. Which variables are being tested in this Test of Independence?
      
   2. What are the hypothesis (H₁), the null hypothesis (H₀), and alpha level?
      

3. What is the df value for the chi-square statistic?
4. What is the population size?
5. Using SPSS and the dataset, ParaFW.csv, conduct a Test of Independence. What is the chi-square statistic and p-value?
   

1. 6. BY HAND! Calculate the chi-square statistic for this test of independence with α = .05.
      
2. 7. Conduct a measure the Effect Size. Is this effect size small, medium, or large?
      

State your decision: Based on your statistical analysis, does this data suggest a significant relationship between belief in free will and belief in the paranormal amongst the budding psychologists at ASU?

17. The lengths of a population of certain HULU shows I watch are normally distributed with a mean running time of 38 minutes and a standard deviation of 11.5.

1. Find the percentage of shows with running times between 26 and 42 minutes.

2.Between what values would you expect to find the middle 80 %

3. Find the percentage of shows with running times below 47.5 minutes

4.Above what value would you expect to find the top 25 %?

5.Find the percentage of shows with running times above 18 minutes.

Absenteeism is a major problem for some companies and in some industries. Suppose a study was conducted on absenteeism in the warehousing industry. Observations on several variables that might be related to absenteeism were collected on 35 major warehouses in the Pacific Northwest.

Absent: The average number of absences per employee for the year (does not include vacation days or confirmed sick days)

Wage: The average annual wage paid to the warehouse employees (does not include manager salaries)

Pct U: Union membership. The percentage of employees who belong to a union at the warehouse.

Good R: 1 if the employee group self-reported a “good” relationship with management; 0 if the employee group self-reported otherwise.

Perform a complete multiple regression analysis to find a model that might be useful for predicting the average number of absences per employee for the year. Perform ALL steps as outlined in class. Use Minitab and show all your work. Use alpha = .10 for any required tests (and show all steps for any required test). STAPLE MULTIPLE PAGES and include all required computer output.

A researcher hypothesizes that caffeine will affect the speed with which people read. To test this, the researcher randomly assigns 8 people into one of two groups: 50mg Caffeine (n1=4) or no Caffeine (n2=4). An hour after the treatment, the 8 participants in the study are asked to read from a book for 1 minute; the researcher counts the number of words each participant finished reading. The following are the data for each group:

50mg Caffeine (group 1)

450 400 500 450

No Caffeine (group 2)

400 410 430 440

Use α-level of .05 to answer the questions below:

i. Draw the sampling distribution of the difference between independent sample means, and locate M1-M2, μ(m1-M2) on the x-axis. What is the value of μ(m1-M2 under the assumption of the null hypothesis; indicate this on the x-axis as well.

j. Given the total df for this problem, what is the critical value of t? Indicate the critical value of t (and its value) in your drawing on (i). Also, indicate what the area is in the tail beyond the critical value of t.

k. Can you reject the null hypothesis?

l. Can you accept the research hypothesis?

1)

A report says that 82% of British Columbians over the age of 25 are high school graduates. A survey of randomly selected British Columbians included 1290 who were over the age of 25, and 1135 of them were high school graduates. Does the city’s survey result provide sufficient evidence to contradict the reported value, 82%?

Part i) What is the parameter of interest?

A. The proportion of all British Columbians (aged above 25) who are high school graduates.
B. Whether a British Columbian is a high school graduate.
C. All British Columbians aged above 25.
D. The proportion of 1290 British Columbians (aged above 25) who are high school graduates.

Part ii) Let pp be the population proportion of British Columbians aged above 25 who are high school graduates. What are the null and alternative hypotheses?

A. Null: p=0.88p=0.88. Alternative: p≠0.88p≠0.88.
B. Null: p=0.82p=0.82. Alternative: p=0.88p=0.88.
C. Null: p=0.82p=0.82. Alternative: p>0.82p>0.82.
D. Null: p=0.88p=0.88. Alternative: p>0.88p>0.88.
E. Null: p=0.82p=0.82. Alternative: p≠0.82p≠0.82 .
F. Null: p=0.88p=0.88. Alternative: p≠0.82p≠0.82.

Part iii) The PP-value is less than 0.0001. Using all the information available to you, which of the following is/are correct? (check all that apply)

A. The reported value 82% must be false.
B. Assuming the reported value 82% is correct, it is nearly impossible that in a random sample of 1290 British Columbians aged above 25, 1135 or more are high school graduates.
C. The observed proportion of British Columbians who are high school graduates is unusually high if the reported value 82% is correct.
D. The observed proportion of British Columbians who are high school graduates is unusually low if the reported value 82% is correct.
E. The observed proportion of British Columbians who are high school graduates is unusually high if the reported value 82% is incorrect.
F. The observed proportion of British Columbians who are high school graduates is unusually low if the reported value 82% is incorrect.
G. Assuming the reported value 82% is incorrect, it is nearly impossible that in a random sample of 1290 British Columbians aged above 25, 1135 or more are high school graduates.

Part iv) What is an appropriate conclusion for the hypothesis test at the 5% significance level?

A. There is sufficient evidence to contradict the reported value 82%.
B. There is insufficient evidence to contradict the reported value 82%.
C. There is a 5% probability that the reported value 82% is true.
D. Both A. and C.
E. Both B. and C.

Part v) Which of the following scenarios describe the Type II error of the test?

A. The data suggest that reported value is correct when in fact the value is incorrect.
B. The data suggest that reported value is correct when in fact the value is correct.
C. The data suggest that reported value is incorrect when in fact the value is correct.
D. The data suggest that reported value is incorrect when in fact the value is incorrect.

Part vi) Based on the result of the hypothesis test, which of the following types of errors are we in a position of committing?

A. Type I error only.
B. Type II error only.
C. Both Type I and Type II errors.
D. Neither Type I nor Type II errors.

2)

(1 point) McBeans magazine recently published a news article about caffeine consumption in universities that claims that 80% of people at universities drink coffee regularly. Moonbucks, a popular coffee chain, is interested in opening a new store on UBC campus. After reading McBeans' article, they will consider opening a store in UBC if more than 80% of the people in UBC drink coffee regularly. A random sample of people from UBC was taken, and it was found that 680 out of 810 survey participants considered themselves as regular coffee drinkers. Does Moonbucks' survey result provide sufficient evidence to support opening a store at UBC?

Part i) What is the parameter of interest?

A. Whether a person at UBC drinks coffee regularly.
B. The proportion of all people at UBC that drink coffee regularly.
C. The proportion of people at UBC that drink coffee regularly out of the 810 surveyed.
D. All people at UBC that drinks coffee regularly.

Part ii) Let pp be the population proportion of people at UBC that drink coffee regularly. What are the null and alternative hypotheses?

A. Null: p=0.84p=0.84. Alternative: p≠0.84p≠0.84.
B. Null: p=0.84p=0.84. Alternative: p>0.80p>0.80.
C. Null: p=0.80p=0.80. Alternative: p>0.80p>0.80 .
D. Null: p=0.84p=0.84. Alternative: p>0.84p>0.84.
E. Null: p=0.80p=0.80. Alternative: p=0.84p=0.84.
F. Null: p=0.80p=0.80. Alternative: p≠0.80p≠0.80.

Part iii) The PP-value is found to be about 0.0025. Using all the information available to you, which of the following is/are correct? (check all that apply)

A. The observed proportion of people at UBC that drink coffee regularly is unusually low if the reported value 80% is correct.
B. Assuming the reported value 80% is incorrect, there is a 0.0025 probability that in a random sample of 810, at least 680 of the people at UBC regularly drink coffee
C. Assuming the reported value 80% is correct, there is a 0.0025 probability that in a random sample of 810, at least 680 of the people at UBC regularly drink coffee.
D. The observed proportion of people at UBC that drink coffee regularly is unusually low if the reported value 80% is incorrect.
E. The observed proportion of people at UBC that drink coffee regularly is unusually high if the reported value 80% is correct.
F. The observed proportion of people at UBC that drink coffee regularly is unusually high if the reported value 80% is incorrect.
G. The reported value 80% must be false.

Part iv) What is an appropriate conclusion for the hypothesis test at the 5% significance level?

A. There is sufficient evidence to support opening a store at UBC.
B. There is insufficient evidence to support opening a store at UBC.
C. There is a 5% probability that the reported value 80% is true.
D. Both A. and C.
E. Both B. and C.

Part v) Which of the following scenarios describe the Type II error of the test?

A. The data do not provide sufficient evidence to support opening a store at UBC when in fact the true proportion of UBC people who drink coffee regularly exceeds the reported value 80%.
B. The data provide sufficient evidence to support opening a store at UBC when in fact the true proportion of UBC people who drink coffee regularly is equal to the reported value 80%.
C. The data provide sufficient evidence to support opening a store at UBC when in fact the true proportion of UBC people who drink coffee regularly exceeds the reported value 80%.
D. The data do not provide sufficient evidence to support opening a store at UBC when in fact the true proportion of UBC people who drink coffee regularly is equal to the reported value 80%.

Part vi) Based on the result of the hypothesis test, which of the following types of errors are we in a position of committing?

A. Type II error only.
B. Both Type I and Type II errors.
C. Type I error only.
D. Neither Type I nor Type II errors.

3)Suppose some researchers wanted to test the hypothesis that living in the country is better for your lungs than living in a city. To eliminate the possible variation due to genetic differences, suppose they located five pairs of identical twins with one member of each twin living in the country, the other in a city. For each person, suppose they measured the percentage of inhaled tracer particles remaining in the lungs after one hour: the higher the percentage, the less healthy the lungs. Suppose they found that for four of the five twin pairs the one living in the country had healthier lungs.Is the alternative hypothesis one-sided or two-sided?one-sided
one-sided or two-sided
two-sided
none of these answersHere are the probabilities for the number of heads in five tosses of a fair coin:

Compute the p-value and state your conclusion.p-value = 0.15625 + 0.03125 = 0.1875 and we have little evidence that individuals living in the country have healthier lungs than those individuals living in cities.
p-value = 0.03125 and we have little evidence that individuals living in the country have healthier lungs than those individuals living in cities.
p-value = 0.15625 and we have little evidence that individuals living in the country have healthier lungs than those individuals living in cities.
p-value = 0.15625 - 0.03125 = 0.125 and we have little evidence that individuals living in the country have healthier lungs than those individuals living in cities.