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1)Descriptive analysis of each of the variables: measures of central tendency, d

ID: 3157303 • Letter: 1

Question

1)Descriptive analysis of each of the variables: measures of central tendency, dispersion and slant.             
2)The density function for the difference between the average production and average beer sales .             
3)The probability that production is not efficient , meaning that sales are greater than production.                 
4)Perform a confidence interval of 95 % for the difference between average production and sales of beers.    
5)Perform a confidence interval of 95 % for the ratio of standard deviations between the average production and sales of beers.               
6)Demonstrate that the average production is less than average sales .                             
7) Perform a hypothesis test to see if the variances between production and average beer sales are different.     

Production Sales (thousands of (thousands iters 6,163,188 6,190,331 6,352,992 6,336,792 6,546,156 6,551,168 6,757,483 6,813,248 7,202,9547,266,495 7,803,946 7,845,630 8,050,985| 8,122,625 8,195,749 8,193,948 8,075,440 8,054,036 8,162,618| 8,161,123 8,219,223 8,223,594 7,991,6047,991,594 8,474,815 8,470,815 8,643,086| 8,623,642 8,436,671 8,464,533 of liters 1 Descriptive analysis of each of the variables: measures of central tendency, dispersion and slant 2 The density function for the difference between the average yield and average beer sales 3 The probability that production is not efficient, ie that sales are greater than production 4 Perform a confidence interval of 95 % for the difference between average production and sales of beers. 5 Perform a confidence interval of 95 % for the ratio of standard deviations between the average production and sales of beers. 6 Demonstrate that the average production is less than average sales 7 Perform a hypothesis test to see if the variances between production and average beer sales are different.

Explanation / Answer

Descriptive statistics using EXCEL.

syntax is,

Enter all the data in EXCEL sheet --> Data --> Data Analysis --> Descriptive statistics --> ok --> Input Range : select data range -->Grouped by : columns --> Output Range : select one empty cell --> click on summary statistics --> Click on confidence level for mean : 95 --> ok

Result is :

We can't find confidence interval for two samples in EXCEL.

Perform a confidence interval of 95 % for the difference between average production and sales of beers.

Here we use t-test for two samples.

This we can done using MINITAB.

steps :

Enter all the data in MINITAB sheet --> Stat --> Basic statistics --> 2-Sample t (Test and confidence Interval) --> Select samples is in different columns --> select in first : production --> select in second : sales --> Assume equal variances --> Options --> Confidence level : 95.0 --> Test difference : 0 --> Alternative : not equal --> ok --> ok

95% CI for difference: (-637380.6, 606358.7)

5)Perform a confidence interval of 95 % for the ratio of standard deviations between the average production and sales of beers.

7) Perform a hypothesis test to see if the variances between production and average beer sales are different.   

This we can done using MINITAB.

Here we have to test the hypothesis that,

H0 : Variances are equal.

H1 : Variances are not equal.

Assume alpha = 5% =0.05

Steps :

Enter all the data in MINITAB sheet --> Stat --> Basic statistics --> 2-variances --> Samples in different columns --> First : select production --> second : select sales --> Options --> Confidence level : 95.0 --> ok --> Storage : select all the options --> ok --> ok


Test for Equal Variances for production, sales


Test for Equal Variances: production, sales

95% Bonferroni confidence intervals for standard deviations

N Lower StDev Upper
production 15 585785 834644 1414677
sales 15 581233 828158 1403683


F-Test (normal distribution)
Test statistic = 1.02, p-value = 0.977


Levene's Test (any continuous distribution)
Test statistic = 0.00, p-value = 0.973

The F test statistc = 1.02

P-value = 0.977

P-value > alpha

Accept H0 at 5% level of significance.

Conclusion : Variances are equal.

2)The density function for the difference between the average production and average beer sales .   

That is the distribution of X1bar - X2bar is also t-test for two samples.

Column1 Column2 Mean 7671794 Mean 7687305 Standard Error 215504.1595 Standard Error 213829.4 Median 8050985 Median 8054036 Mode #N/A Mode #N/A Standard Deviation 834644.0209 Standard Deviation 828157.6 Sample Variance 6.96631E+11 Sample Variance 6.86E+11 Kurtosis -0.9417769 Kurtosis -0.87186 Skewness -0.787791802 Skewness -0.82718 Range 2479898 Range 2433311 Minimum 6163188 Minimum 6190331 Maximum 8643086 Maximum 8623642 Sum 115076910 Sum 1.15E+08 Count 15 Count 15 Confidence Level(95.0%) 462210.4511 Confidence Level(95.0%) 458618.4