An advocacy group claims that Blacks/African-Americans are over-represented in the incarcerated population. In other words, they are claiming that there is a higher percentage of Blacks/African-Americans in the incarcerated population than in the general US population. A random sample of 150 US residents is sampled and 26 identify as Black/African-American. In another random sample of 40 US incarcerated individuals, 14 identify as Black/AfricanAmerican. Is there enough evidence to support the group’s claim at the 1% level of significance?

A. State the claim mathematically. Is the claim the null or alternative hypothesis?

B. State your hypotheses.

C. Determine the test of significance (t-test or z-test) and justify your choice.

D. State the standardized test statistic.

E. State the p-value.

F. State the correct decision of the test.

G. Interpret the decision in the context of the claim.

I really need help as soon as possible with this question, thank you!

In an annual report to investors, an investment firm claims that the share price of one of their bond funds had very little variability. The report shows the average price as $⁢20.00 with a variance of 0.18. One of the investors wants to investigate this claim. He takes a random sample of the share prices for 22 days throughout the last year and finds that the standard deviation of the share price is 0.2207 Can the investor conclude that the variance of the share price of the bond fund is different than claimed at α=0.01 Assume the population is normally distributed.

Step 2: Determine the critical value(s) of the test statistic. If the test is two-tailed, separate the values with a comma. Round your answer to THREE decimal places.

Step 3: Determine the value of the test statistic. Round your answer to three decimal places.

Step 4: Make the decision.

A fish story: The mean length of one-year-old spotted flounder, in millimeters, is 133 with standard deviation of 20, and the mean length of two-year-old spotted flounder is 156 with a standard deviation of 24. The distribution of flounder lengths is approximately bell-shaped.

(a) Anna caught a one-year-old flounder that was 145 millimeters in length. What is the z-score for this length? Round the answers to at least two decimal places.

(b) Luis caught a two-year-old flounder that was 195 millimeters in length. What is the z-score for this length? Round the answers to at least two decimal places.

(c) Joe caught a one-year-old flounder whose length had a z-score of 1.3. How long was this fish? Round the answer to at least one decimal place.

(d) Terry caught a two-year-old flounder whose length had a z-score of −0.6. How long was this fish? Round the answer to at least one decimal place.

1) We are creating a new card game with a new deck. Unlike the normal deck that has 13 ranks (Ace through King) and 4 Suits (hearts, diamonds, spades, and clubs), our deck will be made up of the following.

Each card will have:
i) One rank from 1 to 16.
ii) One of 5 different suits.

Hence, there are 80 cards in the deck with 16 ranks for each of the 5 different suits, and none of the cards will be face cards! So, a card rank 11 would just have an 11 on it. Hence, there is no discussion of "royal" anything since there won't be any cards that are "royalty" like King or Queen, and no face cards!

The game is played by dealing each player 5 cards from the deck. Our goal is to determine which hands would beat other hands using probability. Obviously the hands that are harder to get (i.e. are more rare) should beat hands that are easier to get.

i) How many different ways are there to get a flush (all cards have the same suit, but they don't form a straight)?
Hint: Find all flush hands and then just subtract the number of straight flushes from your calculation above.
The number of ways of getting a flush that is not a straight flush is
DO NOT USE ANY COMMAS

What is the probability of being dealt a flush that is not a straight flush?
Round your answer to 7 decimal places.

j) How many different ways are there to get a straight that is not a straight flush (again, a straight flush has cards that go in consecutive order like 4, 5, 6, 7, 8 and all have the same suit. Also, we are assuming there is no wrapping, so you cannot have the ranks be 14, 15, 16, 1, 2)?
Hint: Find all possible straights and then just subtract the number of straight flushes from your calculation above.
The number of ways of getting a straight that is not a straight flush is  
DO NOT USE ANY COMMAS

What is the probability of being dealt a straight that is not a straight flush?
Round your answer to 7 decimal places.

2) Given the following information, answer questions a - d.
P(A)=0.48P(A)=0.48
P(B)=0.41P(B)=0.41
A and B are independent.
Round all answers to 5 decimal places as needed

a) Find P(A∩B).

b) Find P(A∪B).
c) Find P(A∣B).  

d) Find P(B∣A).  

Given the following information, answer questions e - g.
P(A)=0.48P(A)=0.48
P(B)=0.41P(B)=0.41
A and B are dependent.
P(A|B) = 0.14
Round all answers to 5 decimal places as needed

e) Find P(A∩B).     

f) Find P(A∪B)

g) Find P(B∣A).

SAVE OUTFILE = ‘\\Client\H$\Desktop\car.sav'.

explains what this part does in SPSS

A Gallup poll asked a random sample of 1000 adults nation-wide the following question:: "Are you in favor of the death penalty for a person convicted of murder?" 71% of the people in the sample answered "Yes".

1. A 95% Confidence Interval for the percent of all adults nation-wide in favor of the death penalty is (Hint: Fill in the first blank with the sample % and the second with the margin of error.)

（ ） % +/- （ ）%

A recent CBS New poll randomly sampled 1,142 adults nationwide asking them the following question:

"As you may know, the legal drinking age is 21. Would you approve or disapprove of states lowering the drinking age to 18, if the states felt that would give the police more time to enforce other laws?" 24% answered that they approved.

1. What is the expected value for the percent of all US adults who would say they approve of lowering the drinking age to 18, if the states felt that would give the police more time to enforce other laws? （ ）%

2. What is the SD of the sample? (Round to 3 decimal places.)

3. Calculate the SE of the percentage of people in the sample who answered "Approve". (Round to 2 decimal places.)

A poll is given, showing 75% are in favor of a new building project. If 138 people are chosen at random, answer the following. What is the probability that exactly 103 of them are in favor of a new building project? What is the probability that less than 103 of them are in favor of a new building project? What is the probability that more than 103 of them are in favor of a new building project? What is the probability that exactly 110 of them are in favor of a new building project? What is the probability that at least 110 of them are in favor of a new building project?

Components of a certain type are shipped to a supplier in batches of ten. Suppose that 48% of all such batches contain no defective components, 29% contain one defective component, and 23% contain two defective components. Two components from a batch are randomly selected and tested. What are the probabilities associated with 0, 1, and 2 defective components being in the batch under each of the following conditions? (Round your answers to four decimal places.)

(a) Neither tested component is defective.

1. Complete Table 2 by calculating the expected deaths for Indiana (columns a and b) and Alaska (columns a and d) based on the standard population distribution of the US in 1992. The age-specific deaths are obtained from your calculations in Table 1.

Table 2

Column b will be taken directly from Table 1. Calculate the age-adjusted rates: Add the expected deaths for each state, i.e. columns (c) and (e). Divide the total expected deaths in each state by the total standard population of the US.

Calculate the age-adjusted rates: Add the expected deaths for each state, i.e. columns (c) and (e). Divide the total expected deaths in each state by the total standard population of the US.

7.           Calculate the age-adjusted death rate per 1000 for each state:    (5 points)

In the “HomeSales” dataset, the response variable, sales, depends on six potential predictor variables, sq_ft, adv_cost, inventory, distance, district_size, and storecount. Fit four simple linear regression (SLR) models corresponding to the four predictors, sq_ft, adv_cost, inventory, and distance. Then, for each model, create a normal probability plot and a histogram for the residuals, together with the two residual scatterplots: residuals vs. fitted values and residuals vs. observation order.

What do the residual plots for the model with sq_ft as the predictor indicate about the validity of this regression model and assumptions made about the errors?

What do the residual plots for the model with adv_cost as the predictor indicate about the validity of this regression model and assumptions made about the errors?

What do the residual plots for the model with inventory as the predictor indicate about the validity of this regression model and assumptions made about the errors?

What do the residual plots for the model with distance as the predictor indicate about the validity of this regression model and assumptions made about the errors?

One objective of this analysis is to obtain an appropriate simple linear regression model that can be used to estimate the average sales based on a single predictor. State your “best” choice based on your conclusions in parts (a)–(d).

Complete the table below, using the regression analysis results of the four simple linear regression models considered in parts (a)–(d). Based on the table entries, would you change your “best” choice from part (e).

A model including the predictor variable adv_cost is of specific interest. Obtain appropriate residual plots and determine if adding either district_size or storecount as an additional predictor to the SLR model with predictor adv_cost is likely to improve its fit.

Problem 16-05 (Algorithmic)

A major traffic problem in the Greater Cincinnati area involves traffic attempting to cross the Ohio River from Cincinnati to Kentucky using Interstate 75. Let us assume that the probability of no traffic delay in one period, given no traffic delay in the preceding period, is 0.8 and that the probability of finding a traffic delay in one period, given a delay in the preceding period, is 0.65. Traffic is classified as having either a delay or a no-delay state, and the period considered is 30 minutes.

1. Assume that you are a motorist entering the traffic system and receive a radio report of a traffic delay. What is the probability that for the next 60 minutes (two time periods) the system will be in the delay state? Note that this result is the probability of being in the delay state for two consecutive periods. If required, round your answer to three decimal places.
   
   =0.4225
2. What is the probability that in the long run the traffic will not be in the delay state? If required, round your answers to three decimal places.

Number of defective monitors manufactured in day shift and afternoon shift is to be compared. A sample of the production from six day shifts and eight afternoon shifts revealed the following number of defects.

Day 4 5 8 6 7 9

Afternoon 9 8 10 7 6 14 11 5

Is there a difference in the mean number of defects per shift? Choose an appropriate significance level.

(a) State the null hypothesis and the alternative hypothesis.

(b) What is the decision rule?

(c) What is the value of the test statistic?

(d) What is your decision regarding the null hypothesis?

(e) What is the p-value? (f ) Interpret the result.

(g) What assumptions are necessary for this test?

(Typed answer preferred)

Statistics and Graphical Displays

Valencia Orange Price Comparison

You have been hired as a consultant to determine who ABC Grocery Store should be ordering Valencia Oranges from.

To: Statistician

From: ABC Grocery Store

Please advise us on which company to use as our orange distributor. Three highly recommended distributors have provided us with statistical data on the weekly prices for one load of Valencia oranges per week for a ten-week period last year. Prices fluctuate according to availability, and we would like to use the company with the lowest overall price and the least amount of fluctuation. We would like your written report showing your results and a detailed recommendation as to which company we should choose.

Here are the prices, listed as price in dollars per crate:

You must type in and analyze the data for each company.    

Helpful directions:

1. Analyze the data for each company: frequency, relative frequency, mean, median, mode, standard deviation, and range. (I already made a chart which is show right below this question for this and answered it. I just need help with the rest please)

2. 	The Fruit Guys	Sunny Oranges	Tree Groves
   Mean	327	318	317.9
   Median	327.5	315	315
   Mode	350	315	290,320
   Standard Deviation	20.761	20.273	22.421
   Range	65	60	69
   Frequency	3270	3180	3179
   Relative Frequency	355	350	359

3. You need to decide which statistics to compare to determine the overall lowest price and the least fluctuation. Create and include at least two charts that will be useful to best support your conclusions. (PLEASE DRAW THE CHARTS, THANK YOU!)
4. Write a brief informative letter in response to the request from ABC Grocery answering their request. Be sure to include:
   1. A very detailed explanation of the data and the conclusions you came to. You should use the statistics you calculated to make this decision. (HELPPPPP PLEASEEEE! THANK YOU******)
   2. Charts to support your explanation.
5. Attach copies of the Excel pages or embed the Excel work in your letter of response.

A personnel director claims that the distribution of the reasons withers leave their job is different from the distribution: 41% limited advancement; 25% lack of recognition; 15% low salary/benefits; unhappy with management 10%; 9% bored. You randomly select 200 workers who recently left their jobs and record each worker’s reasons for doing so. The table below show the results. At the 0.01 level of significance, test the personnel director’s claim.

Expected Frequencies for each?