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.
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%) 458618.4Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.