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?

A study might compare the rates of microbiologic cure of three different antibiotics used for urinary tract infection, as shown in the following table:

1. Are the variables quantitative or qualitative?
2. Which statistical test is appropriate to use on these data?
3. What are the null & the alternative hypotheses, here? Use 10% level of significance
4. Carry out the hypothesis test(s) in question in above c.

Is there is a relationship between which antibiotic the patient took and achieving microbiologic cure?                

For the problems 1 -6

Consider the data set   

16, 26, 31, 32, 32, 32, 42, 47, 47, 47, 50, 50 (already put in increasing order)

Compute the following:

1/   The mode:

A/ 47       B/ 32           C/ Bimodal       D/ 42  

2/   The median:

A/ 42       B/ 37           C/ 32           D/ 47  

3/   The mean:

       A/ 37.7       B/ 37           C/ 36           D/ 36.2

4/   The standard deviation:

       A/ 10.5       B/ 12          C/ 14           D/ 11  

5/   The mid-range:

A./ 17       B/ 20.5         C/ 33           D/ 34      
6/   If x = 42 , the standard deviation s = 12 and the mean = 67, then the z-score ( the standard score) of x is

A./ 2.28       B/ - 1.00       C/ 3.52       D/ -2.08
  
7/   In the set of data : 2, 3, 35, 5, 8, 9,10, 10,12,14,16, is the value 35 outlier?

A/ No, upper limit for outlier is 27.5       B/ Yes, upper limit for outlier is 27.5
C/ No, upper limit for outlier is 24.5       D/ Yes, upper limit for outlier is 32.1
  

For the problems 8 -13: Consider the set of 15 data ( in increasing order )

   10, 15, 19, 20, 21, 21, 29, 29, 30, 30, 33, 39, 40, 50, 50.

( It is better to enter this data set into a calculator to find the needed values to answering the following questions )

8/   Find ( the value x which separates the bottom 30th percentile )      

A./ 70       B/ 21           C/ 29.5         D/ 53      

9/   Find the percentile ( kth percentile ) of the value x = 30.

A/ 53 percentile   B/ 82 percentile C/ 38 percentile   D/ 60 percentile  

10/   The third quartile () is:

   A./ 39       B/ 17           C/ 40         D/ 18      

11/   The inter-quartile range ( IQR) is:          

A./ 17       B/ 21           C/ 19         D/ 59  

12/   The sample variance is approximate to ( round to whole number )

A./ 11       B/ 148       C/ 12         D/ 142
      

13/   Approximate the value of x if its z-score is 0.83 ( Use the formula )

  
A./ 35       B/ 39           C/ 19         D/ 25      
14/   For the data set 8, 6, 29, 3, 9, 23, 15, 18, 5, 3, 22, 27, 4, 2 and 22 the midrange is

  
A./ 16       B/ 11           C/ 15         D/ 18      

15/   By the Empirical Rule, in a city of 62,000 people, the number of people below the mean by more than 1 standard deviation is:

A./ 41,160      B/ 9, 920       C/ 21,080        D/ 6,200      
Questions 16-18 : Use the distribution in the form of the stem-leaf plot

         
Stem   Leaves   

1478   
01237888  
189   

16/   The mid-point of the third class is

   A./ 32       B/ 36           C/ 34.5         D/ 35      

17/   The median is

   A./ 24       B/ 23           C/ 25           D/ 5
      
18/   The relative frequency for the third class is:

A./ 20%       B/ 50%        C/ 66%         D/ 40%

19/   The heights of a group of professional basketball players are summarized in the frequency distribution below. Find the mean height from this frequency table.

           Height s ( in)   Frequency
  
4
6
8
79-81       2

A./ 75.2 in       B/ 76.8 in       C/ 74.0 in       D/ 77.5 in

20/   The temperatures ( in ºF ) in a room is recorded at the top of hours are

   67, 68, 70 , 5, 77, 77, 78, 80, 78, 79, 74, 74. Choose best answer:
  
   a/ It is a typo
   b/ highest temperature is probably 95
   c/ 5 is not an outlier
   d/ 5 is an outlier

21/   The variance of 6 washing machines with prices: $ 800, $784, $ 1,235, $860, $1,036 and $770 is

A/ 196.4       B/ 34,295.3       C/ 26,002.7       D/ 185.2

22/   The coefficient of variation ( round to closest %) for the set of data :

1, 3, 3, 5, 5, 6, 7, 8, 9 ,12, 15, 24 is

A 74%       B/ 67%       C/ 24%       D/ 78 %

23/   Human body temperatures have the mean of 98.2º and a standard deviation of 0.6º.
   Amy’s temperature can be described by z = 0.9. What is her temperature?

   A/   98.2º       B/ 97.8º       C/ 98.7º       D/ 99.3º

24/   The upper bound for the outlier for the data set
-11, 14, 22, 22, 22, 23, 31, 31, 42, 44, 44, 75 is

A/ 74.5           B/ 75           C/ 84       D/ 68
                                  
25/   The box-plot of a data with 5- point summary 2, 6, 8, 11, 18
  

   A/is positive skewed.       B/ is negative skewed.
   C/ is symmetric       D/ perfect skewed

Let X ~ N(196; 19). Find:

(a) P(X </= 223)

(b) P(143 < X < 206)

(c)  P(|X-196|> 30)

Background

The 2016 US Presidential Election brought considerable attention to the phenomenon of “fake news”: entirely fabricated and often partisan content that is presented as factual. Researchers evaluated one mechanism that may contribute to the believability of fake news: fluency via prior exposure. Using an actual fake news headline presented as it was seen on Facebook (Kid Rock launches campaign to run for U.S. Senate in 2018), the researchers hypothesized that previous exposure to the fake news story would increase perceptions of accuracy. Subjects were pre-screened to determine in which of 3 groups they belonged: 1) no previous exposure to the fake news story, 2) previous exposure to the fake news story and had not heard that the story was, in fact, fake, or 3) previous exposure to the fake news story but had heard that the story was, in fact, fake. They recorded perception of the accuracy of the news story (ranging from 1 (definitely false) to 6 (definitely true)).

Please complete all empty boxes in the tables below.

Data

One-way ANOVA (please show your work!)

Post-hoc results using the Tukey test

Full interpretation of the results

A parabolic satellite dish reflects signals to the dish’s focal point. An antenna designer analyzed signals transmitted to a satellite dish and obtained the probability density function

f(x)=cæ1- 1 x2öfor 0<x<2,whereXisthedistance(inmeters)fromthecentroidofthe ç 16 ÷

èø

dish surface to a reflection point at which a signal arrives. Determine the following:

1. Value of c that makes f (x) a valid probability density function

2. ?(? < 0.4

3. ?(0.1<?<0.4

4. ?(?)

5. ?(?)

For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

A random sample of 5260 permanent dwellings on an entire reservation showed that 1585 were traditional hogans.

(a) Let p be the proportion of all permanent dwellings on the entire reservation that are traditional hogans. Find a point estimate for p. (Round your answer to four decimal places.)


(b) Find a 99% confidence interval for p. (Round your answer to three decimal places.)

Give a brief interpretation of the confidence interval.

1% of the confidence intervals created using this method would include the true proportion of traditional hogans.99% of the confidence intervals created using this method would include the true proportion of traditional hogans.    99% of all confidence intervals would include the true proportion of traditional hogans.1% of all confidence intervals would include the true proportion of traditional hogans.

(c) Do you think that np > 5 and nq > 5 are satisfied for this problem? Explain why this would be an important consideration.

No, the conditions are not satisfied. This is important because it allows us to say that p̂ is approximately binomial.No, the conditions are not satisfied. This is important because it allows us to say that p̂ is approximately normal.    Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately binomial.Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately normal.