Homework Help for Statistics

Consider a sample of 47 football games, where 30 of them were won by the home team. Use a 0.01 significance level to test the claim that the probability that the home team wins is greater than one-half.

 

 

 

 

A genetic experiment involving peas yielded one sample of offspring consisting of 400 green peas and 165 yellow peas. Use a 0.05 significance level to test the claim that under the same circumstances. 234, of offspring peas will be yellow. Identify the null hypothesis, alternative hypothesis, test statistic, P.value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P.value method and the normal distribution as an approximation to the binomial distribution.

A.  

B.    

 

C.  

D.  

E.  

F.  

Consider a drug that is used to help prevent blood clots in certain patents. In clinical trials, among 6184 patients treated with this drug, 161 developed the adverse reaction of nausea. Use a 0.01 significance level to test the claim that 3% of users develop nausea. Does nausea appear to be a problematic adverse reaction?

Identify the null and alternative hypotheses for this test. Choose the correct answers below. 

A.  

B.  

C.  

D.  

2. A certain drug is used to treat asthma. In a clinical trial of the drug, 24 of 299 treated subjects *** headaches (based on data from the manufacturer). The accompanying calculator display shows results from a test of the claim that less than 11% of treated subjects experienced headaches. Use the normal distribution as an approximation to the binomial distribution and assume a 0.05 significance level to complete parts (a) through (e) below.

◯ A. : p = 0.11

◯ B. : p 0.11

◯ C. : p > 0.11

◯ D. : p < 0.11

Decide whether to reject the null hypothesis. Choose the correct answer below:

◯ A. Fall to reject the null hypothesis because the P-value is greater than the significance level, .

◯ B. Fail to reject the null hypothesis because the P-value is less than or equal to the significance level, .

◯ C. Reject the null hypothesis because the P-value is less than or equal to the significance level, .

◯ D. Reject the null hypothesis because the P-value is greater than the significance level .

 

e. What is the final conclusion?

◯ A. There is not sufficient evidence to warrant rejection of the claim that less than 11% of treated subjects experienced headaches.

◯ B. There is sufficient evidence to warrant rejection of the cliam that less than 11% of treated subjects experienced headaches

A county is considering rasing the speed limit on a road because they claim that the mean speed of vehicles is greater than 45 miles per hour. A random sample of 20 vehicles has a mean speed of 50 miles per hour and a standard deviation of 5.2 miles per hour. At = 0.10, do you have enough evidence to support the county's claim? Complete parts (a) through (d) below.

A. Reject  because the P-value is greater than the significance level, 0.10.

B. Reject because the P-value is less than the significance level, 0.10.

C. Fail to reject because the P-value is greater than the significance level, 0.10.

D. Fail to reject because the P-value is less than the significance level, 0.10.

A study was conducted to determine the proportion of people who dream in black and white instead of color. Among 307 people over the age of 55, 72 dream in black and white, and among 289 people under the age of 25, 20 dream in black and white. Use a 0.05 significance level to test the claim that the proportion of people over 55 who dream in black and white is greater than the proportion for those under 25. Complete parts (a) through (c) below.

A bin contains 400 colored erasers that fit on the ends of pencils. The numbers of erasers of each color is as follows.

color      Green Blue Red Yellow

  Number   88 60 160 92

a) A random sample of 25 erasers is selected, with replacement, from the bin, find the probability that:

(i) exactly 2 erasers are green;

(ii) at most 3 erasers are blue (4 decimal) ;(use excel and write the function in answer sheet)

(iii) between 8 erasers and 12 erasers, inclusive, are red. ;(use excel and write the function)

Question 1 - to be completed in Jupyter 

a)

(i) Provide a visual summary of each respective variable, and explain why your chosen method to visualise the data is appropriate for this type of data. [2] 

(ii) Comment on the results of your summaries. [1] 

(iii) Provide a scatterplot of y versus x. Give meaningful labels to the axes. [1] 

(iv) Do you think a simple linear regression model of y versus x would be a good fit to the data? Explain why, or why not

b) Find appropriate transformations for the data. In particular:

(i)  Given your results from part (a), suggest three possible transformations for y and explain why these would be reasonable to try. [1]

(ii)  Provide scatterplots of each of your transformed responses versus x. Explain which, if any, of these look promising for fitting a simple linear regression model, possibly after transforming x. If none of them seem suitable, suggest one further transformation and try it, giving a reason for your choice. [3]

(iii)  Select the two most promising looking transformations of y from above and, if necessary, transform x appropriately. Provide scatterplots of the transformed responses versus the possibly transformed explanatory variables and comment on them. If necessary, try different transformations of x. [2]

(c) Carry out a regression analysis of the data. In particular:

(i)  Assume a senior statistician had decided to try the following two sets of transformations:
T1: Inverse square-root transformation of y and inverse transformation of x
T2: Inverse transformation of y and inverse transformation of x

Fit simple linear regression models, M1 and M2, to the two transformed data sets T1 and T2, respectively, and use appropriate residual plots to check if the assumptions of the simple linear regression model hold. [6]

(ii)  Based on your residual analysis, select your preferred model among M1 and M2 and provide the fitted model equation. [2]

(iii)  Is there evidence of a linear relationship between the (transformed) response and the (transformed) explanatory variable in this model? Justify your answer. [2]

(d) A new industrial establishment from the same sector is to be opened soon, and HR is hiring 1600 workers.

(i)  Predict how many supervisors will be needed according to your model, and provide a 95% prediction interval. [4]

(ii)  Would it be reasonable if HR hired 176 supervisors? Explain why, or why not. [1]

(iii)  If HR approached you to predict how many supervisors they would need if they were hiring 2600 workers, what should be your response?

x y 294 30 247 32 267 37 358 44 423 47 311 49 450 56 534 62 438 68 697 78 688 80 630 84 709 88 627 97 615 100 999 109 1022 114 1015 117 700 106 850 128 980 130 1025 160 1021 97 1200 180 1250 112 1500 210 1650 135    

Give four properties of a good estimator

14 Consider the following population model that satisfies the CNLRM assumptions:  

N(0,1)

What is the mean and variance of ?

13.  Using a data set of 81 observations, we estimate a historical regression equation as . Suppose that = 50, = 300, and  

Which of the following is a possible confidence interval for the mean prediction of given = 55?

12 Why is it recommended that you do not deviate too far from the mean value of X when using a historical regression equation to predict a future value of Y?

10 Using a data set of 81 observations, we estimate a historical regression equation as . Suppose that = 50, , and = 20

2  Consider a classical normal linear regression model (CNLRM): , where . Data are given in the table below. Calculate the 90% confidence interval for .

 

 

 

 

 

 

 

 

1  Consider a classical normal linear regression model (CNLRM): , where . Data are given in the table below. Calculate the 90% confidence interval for .