Question

In: Statistics and Probability

Consider the data below: 302.0207, 306.9998, 300.8687, 270.4524, 259.5252, 288.0257, 283.3269, 294.9006, 292.8622, 322.8245, 329.5085, 313.5145,...

Consider the data below:

302.0207, 306.9998, 300.8687, 270.4524, 259.5252, 288.0257, 283.3269, 294.9006, 292.8622, 322.8245, 329.5085, 313.5145, 307.6594, 325.7587, 354.1881, 324.6396, 276.2345, 283.0315, 278.8270, 298.1269

a. What is your BOOTSTRAP estimate of the mean and standard error of the mean?  boot:_____  μboot:_____

b. What is your two-sided 95% BOOTSTRAP CI for the mean?  loboot:_____  hiboot:_____

c. What is your one-sided lower 99% BOOTSTRAP CI for the mean? ? loboot:_____

d. What is your one-sided upper 62% BOOTSTRAP CI for the mean? hiboot:_____

Solutions

Expert Solution

a)

sample std dev ,    s = √(Σ(X- x̅ )²/(n-1) ) =   23.1688          
Sample Size ,   n =    20          
Sample Mean,    x̅ = ΣX/n =    300.6648          
                  
degree of freedom=   DF=n-1=   19          
                  
Standard Error , SE = s/√n =   23.1688   / √    20   =   5.1807

b)

Level of Significance ,    α =    0.05          
degree of freedom=   DF=n-1=   19          
't value='   tα/2=   2.0930   [Excel formula =t.inv(α/2,df) ]      
                  
Standard Error , SE = s/√n =   23.1688   / √   20   =   5.180712
margin of error , E=t*SE =   2.0930   *   5.18071   =   10.843356
                  
confidence interval is                   
Interval Lower Limit = x̅ - E =    300.66   -   10.843356   =   289.821414
Interval Upper Limit = x̅ + E =    300.66   -   10.843356   =   311.508126
95%   confidence interval is (   289.82   < µ <   311.51   )

c)

Level of Significance ,    α =    0.01          
degree of freedom=   DF=n-1=   19          
't value='   tα/2=   2.8609   [Excel formula =t.inv(α/2,df) ]      
                  
Standard Error , SE = s/√n =   23.1688   / √   20   =   5.180712
margin of error , E=t*SE =   2.8609   *   5.18071   =   14.821679
                  
confidence interval is                   
Interval Lower Limit = x̅ - E =    300.66   -   14.821679   =   285.843091

d)

Level of Significance ,    α =    0.38          
degree of freedom=   DF=n-1=   19          
't value='   tα/2=   0.8988   [Excel formula =t.inv(α/2,df) ]      
                  
Standard Error , SE = s/√n =   23.1688   / √   20   =   5.180712
margin of error , E=t*SE =   0.8988   *   5.18071   =   4.656514
                  
confidence interval is                   

Interval Upper Limit = x̅ + E =    300.66   -   4.656514   =   305.321284

------------------------------------

DEAR STUDENT,

IF YOU HAVE ANY QUERY ASK ME IN THE COMMENT BOX,I AM HERE TO HELPS YOU.PLEASE GIVE ME POSITIVE RATINGS

*****************THANK YOU***************


Related Solutions

Consider the two separate samples given in the data set (samplecomparison.xlsx). Answer the questions below. Data...
Consider the two separate samples given in the data set (samplecomparison.xlsx). Answer the questions below. Data listed below. The range of the first data set is _____ . The variance of the first data set is ____ . (Round to three decimal places as needed) The standard deviation of the first data set is _____ . (Round to three decimal places as needed) The range of the second data set is _____ . The variance of the second data set...
Consider the data below of inches of rainfall per month for three different regions in the...
Consider the data below of inches of rainfall per month for three different regions in the Northwestern United States: Plains Mountains Forest April 24.6 12.9 9.6 May 16.9 17.8 16.4 June 18.5 15.4 18.3 July 17.4 11.2 12.7 August 16.1 13.7 15.2 Using SPSS, perform an ANOVA test the hypothesis that there is not the same amount of rainfall in every region in the Northwestern United States with a significance level of 0.10. What are the two degrees of freedom...
Answer the following questions: Consider the data below for a hypothetical economy. All figures are in...
Answer the following questions: Consider the data below for a hypothetical economy. All figures are in billions of dollars. Real Domestic       Aggregate                                                                                       Aggregate     Output               Expenditures (C + Ig),                                                                   Expenditures (C + Ig + Xn),       (GDP = DI)              Private, Closed Economy       Exports, X      Imports, M          Private, Open Economy ($ Billions)                     ($ Billions)                        ($ Billions)     ($ Billions)                ($ Billions)                                                                               200                               245                                   30                    15                         ________                           250                              ...
Consider the data provided in the table below, which shows years of education and income for...
Consider the data provided in the table below, which shows years of education and income for ten individuals. Education Income(1) Income(2) 10 15,000 15 12 20,000 20 12 35,000 35 12 40,000 40 12 60,000 60 16 50,000 50 16 60,000 60 16 70,000 70 18 60,000 60 21 80,000 80 A) Calculate the covariance and correlation of education and income, using the “Income1” column for income, which is measured in dollars. B) Calculate the covariance and correlation of education...
Consider the time-series data in columns A and B on the below (picture). Week (A) Value...
Consider the time-series data in columns A and B on the below (picture). Week (A) Value (B) 1 24 2 13 3 20 4 12 5 19 6 23 7 15 a. Using the naive method, develop a forecast for this time series. Compute MSE and MAPE. Show the forecast for week 8. b. Using all previous values, develop a forecast for this time series. Compute MSE and MAPE. Show the forecast for week 8. c. Develop a three-week moving...
Consider the time-series data in columns A and B on the below (picture). Week (A) Value...
Consider the time-series data in columns A and B on the below (picture). Week (A) Value (B) 1 24 2 13 3 20 4 12 5 19 6 23 7 15 a. Using the naive method, develop a forecast for this time series. Compute MSE and MAPE. Show the forecast for week 8. b. Using all previous values, develop a forecast for this time series. Compute MSE and MAPE. Show the forecast for week 8. c. Develop a three-week moving...
Consider the data below of inches of rainfall per month for three different regions in the...
Consider the data below of inches of rainfall per month for three different regions in the Northwestern United States: Plains Mountains Forest Plains                   Mountains          Forest March                  14.8                      12.6                      11.0 April                     21.4                      13.0                      9.7 May                      17.1                      18.1                      16.5 June                     18.9                      15.7                      18.1 July                       17.3                      11.3                      13.0 August                 16.5 14.0                      15.4 September 16.9 16.7 14.2 Using SPSS, perform a two-sample t-test to test the...
Consider the following hypothetical data in the table below describing a survey in which dog and...
Consider the following hypothetical data in the table below describing a survey in which dog and cat owners are asked whether they go for daily walks. Assume that we want to use a 0.01 significance level to test the claim that whether you own a dog or a cat is independent of whether you take a daily walk (based on Concepts and Applications of two-way table hypothesis tests, Daily walk No Daily walk Dog owner 95 15 Cat owner 40...
Consider the following data on income and savings in your answers to the questions below: Income...
Consider the following data on income and savings in your answers to the questions below: Income ($ thousands) Savings ($ thousands) 50 10 51 11 52 13 55 14 56 15 58 15 60 16 62 16 64 17 67 17 Using excel, calculate the correlation coefficient for the same. Interpret this correlation coefficient and describe the relationship between income and savings. Show a scatter diagram of the relationship between income and savings.
Consider the data below of inches of rainfall per month for three different regions in the...
Consider the data below of inches of rainfall per month for three different regions in the Northwestern United States: Plains Mountains Forest March 14.8 12.6 11.0 April. 21.4 13.0 9.7 May 17.1 18.1 16.5 June 18.9 15.7 18.1 July 17.3 11.3 13.0 August 16.5 14.0 15.4 September 16.9 16.7 14.2 Using SPSS, perform a two-sample t-test to test the hypothesis that there is not the same amount of rainfall in both the Mountains and the Forest regions in the Northwestern...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT