Printed circuit cards are placed in a functional test after being populated with semiconductor chips. Suppose that there are 8 blue credit cards, 6 red credit cards and 4 blue debit cards in a box. It is known that color and card type are to be independent when a card is selected at random from this box.

a) How many red debit cards must be present?

b) Suppose that, 5 cards are randomly selected in a row with replacement. What is the probability that 2 blue credit cards and 2 blue debit cards are selected?

c) Suppose that, 5 cards are randomly selected in a row without replacement. What is the probability that 2 blue credit cards and 2 blue debit cards are selected?

Suppose the length in cm of a male soccer player's foot follows a Normal distribution with mean 31 and variance 25. Suppose the length in cm of a female soccer player's foot follows a Normal distribution with mean 26 and variance 16. A male and female soccer player are selected at random. What is the probability the female player has a longer foot than the male player?

Question 13 options:

Independently of one another, a randomly surveyed individual can be a non-smoker, a light smoker, or a heavy smoker with probabilities 50%, 40% and 10%, respectively. Suppose we randomly survey a sample of 100 people. Given that 34 of them are light smokers, what is the expected number of heavy smokers?

Question 14 options:

The Princess Theatre has 280 seats. 200 tickets are sold for the new popular movie: The Attack of the Goose. Despite every attendee having an assigned seat, they all decide to sit in seats at random. Find the variance of the number of people sitting in their assigned seat. (Hint: use indicator variables)

Question 15 options:

(Please answer without using MINITAB)

Police cars, ambulances, and other emergency vehicles are required to carry road flares. One of the most important features of flares is their burning times. To help decide which of four brands on the market to use, a police laboratory technician measured the burning time for a random sample of 10 flares of each brand. The results were recorded to the nearest minute.

a. Can we conclude that differences exist between the burning times of the four brands of flares?

b. Apply Fisher’s LSD method with the Bonferroni adjustment to determine which flares are better.

c. Repeat Part b using Tukey’s method.

DATA

1. You have been asked to ascertain whether there is a relationship between income level and the amount of money donated to the campaign. Sample data concerning these two categorical variables is given in appendix three below. The numbers in the table represent the numbers of supporters in various income categories who have donated certain amounts of money. At both the 2% and 5% levels of significance, is there evidence of a statistical relationship between income level and amount of money donated to the campaign?

                                                            Income Level

Amount Donated <20K [20K,40) [40K,60K) [60K,80K) ≥80K

[$0,$50)                     35        30              18             10             22                      

[$50,$100                  12        25              26             9              18                      

[$100,$150)               6         20              27             7               5                       

[$150,$200)               7         16              25             10              8                       

[$200,$250)               9         8               11             16              7                                   

[$250,$300)               10        7                8              19             13                      

≥$300                         17        9                8              14             19

The following data show the brand, price ($), and the overall score for six stereo headphones that were tested by a certain magazine. The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from 0 (lowest) to 100 (highest). The estimated regression equation for these data is

ŷ = 23.659 + 0.323x,

where x = price ($) and y = overall score.

(a)

Compute SST, SSR, and SSE. (Round your answers to three decimal places.)

SST = SSR = SSE =

(b)

Compute the coefficient of determination

r².

(Round your answer to three decimal places.)

r²

=

Comment on the goodness of fit. (For purposes of this exercise, consider a proportion large if it is at least 0.55.)

The least squares line provided a good fit as a small proportion of the variability in y has been explained by the least squares line.The least squares line provided a good fit as a large proportion of the variability in y has been explained by the least squares line.     The least squares line did not provide a good fit as a small proportion of the variability in y has been explained by the least squares line.The least squares line did not provide a good fit as a large proportion of the variability in y has been explained by the least squares line.

(c)

What is the value of the sample correlation coefficient? (Round your answer to three decimal places.)

what are some best statistical softwares which give step by step answers for hypothesis testing chi square goodness of fit,confidence interval etc

PART 3 - Create a confidence interval for a proportion.
Investigate the proportion of married patients.

3a. Write a reason why you would want to estimate this population proportion. What can be learned?

3b. State the sample size, n, and the sample proportion, "p bar" (p with a line over it).

3c. Calculate a 95% confidence interval for the population proportion, p. Report at least four decimal places.

*M = Married.

*S = Single.

*DWS = Divorced, Widowed, or Separated

The operating time of a machine manufactured by company A is a random variable (Unit: years) with a standard distribution of N (5; 3,25).
a. A person who has purchased this device has used it for 2 years, calculating the probability that he or she will use it for at least 4 more years
b. The company warranty for 3 years. Calculate the percentage of products that are warranted by the company
c. A person who buys 10 units of this company, calculated the probability of having no more than 2 machines must be warranted in these 10 machines.
d. Among 10,000 products of company A, the probability of having no more than 800 of these 10,000 products must be covered by a warranty

Stadistics

1. A statistics student takes a poll at a local Starbucks to find out if they support the President’s decision for declaring the construction of a southern border wall a national emergency. He polls every fifth person that walks into the coffee shop. Why wouldnʹt this sample be representative of the entire US voting population?

2. There are many websites devoted to polling public opinion on a wide range of topics from politics to consumer preferences. Why are these biased with respect to the general U.S. population? Explain.

3. Identify the sampling technique used to obtain a sample from random, systematic, stratified or convenience sampling. Write the sampling technique in the blank provided. ______________ A group of people are classified according to the county where they live and then random samples of people from each county are taken.

______________ A lottery ball is selected out an air machine. The valve is open, balls are blown into the tube; they are then transferred through another clear tube into a display area for reading.

______________ The first 10 people to arrive at a City Council meeting are surveyed to find out their opinion on a proposed bond referendum.

______________ A quality control supervisor pulls every 20th widget off an assembly line to test for defects.

Write down a clear ‘Research Problem’ (This should be a clear statement mentioning the variable and the Hypothesis Test you intend to perform on it.)     

And perform Hypothesis Testing for the research problem. Use your own confidence/significance level, type of test and any other data you need to conduct the hypothesis test.

Show all your work clearly, including calculations, sketch of the normal curve, the chosen test and the values of level of significance, critical value etc.                 

Summarize the results (What do the test results indicate – Reject the Null hypothesis OR Fail to reject the Null Hypothesis?). Write a Final Conclusion connecting your results obtained above with the stated “Research Problem”

What are the conditions required to apply the multiple regression test?
how to apply it using ANOVA table?

One obervation is taken from the probability model. f(x;θ)=((θ/2)^|x|)*((1-θ)^(1-|x|)) for x=-1,0,1 and θ ∈ [0,1]. We find that the MLE of θ is |x|.

Now consider T(X) where T(X)=2 when x=1 and T(X)=0 otherwise. Show that the MLE of θ has a smaller variance than T(X).

The average time to run the 5K fun run is 22 minutes and the standard deviation is 2.5 minutes. 49 runners are randomly selected to run the 5K fun run. Round all answers to 4 decimal places where possible and assume a normal distribution.

1. What is the distribution of XX? XX ~ N(,)
2. What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
3. What is the distribution of ∑x∑x? ∑x∑x ~ N(,)
4. If one randomly selected runner is timed, find the probability that this runner's time will be between 22.0643 and 22.4643 minutes.
5. For the 49 runners, find the probability that their average time is between 22.0643 and 22.4643 minutes.
6. Find the probability that the randomly selected 49 person team will have a total time more than 1053.5.
7. For part e) and f), is the assumption of normal necessary? YesNo
8. The top 10% of all 49 person team relay races will compete in the championship round. These are the 10% lowest times. What is the longest total time that a relay team can have and still make it to the championship round? minutes

3. Create the printout for testing whether the mean closing price of all NYSE stocks differs from the mean closing price of all NASDAQ stocks and attach it here. Answer the following questions regarding this printout:

1. State the assumptions necessary for this printout to be valid. (You don’t need to state that the samples were randomly and independently selected. We know that they were from part 1 of the project!)

b.   Use the confidence interval to make a statement regarding the relationship between the population means. Make sure to include your confidence level in your statement