Business Statistics - Essay Example

Business Statistics Question i) The mean Chart plot for the 7 batches of 25 each show that four batches had means higher than 3.5g, which is the mean recommended for each cup. The trend suggests that as more batches of 25 are produced, the variation in the grams of logo paint used becomes greater. To reduce this variation, the production process can produce only three batches of 25 per interval. (ii) The 7 batches of 50 however has little variation in the logo paint weight. Four batches have logo paints weight equal to or less than 3.

5g, which means massive productions per batch reduces the chance of putting more paint weight in a cup. Question 2 Confidence interval of Mu with known sigma gives us CI of , while the confidence interval of Mu with unknown sigma gives us CI of . This is based on a random sample of 20 from the entire population of 500. The difference is due to the: Test statistic for known sigma is this is assumed to follow a standard normal distribution. While the test statistic for unknown sigma makes uses the sample standard deviation under the assumption of a t-distribution.

The two different distribution is what brings about the different confidence intervals. Question 3 (a) Null Hypothesis: There is no statistically significant difference (in the mean weight) between Richmond, Kentucky and the US. Alternative Hypothesis: There is a statistically significant difference (in the mean weight) between Richmond, Kentucky and the US. In this particular case let’s assume we don’t know sigma and therefore conduct a t-test Test statistic under Ho. Since this value is less than 1.

753 (the upper 5% point of distribution) so we have sufficient evidence to accept the null hypothesis at the 5% level. (b) Null Hypothesis Richmond, Kentucky mean is not statistically significantly higher than the US, Alternative Hypothesis Richmond, Kentucky mean is statistically significantly higher than the US, Test Statistic under Ho. This value is less than 1.6449 (the upper 5% point of a distribution), so we have insufficient evidence to reject Ho at the 5% level. Question 4 Let mean of Lexington, Kentucky be and mean of Richmond, Kentucky be Null Hypothesis: There is no statistically significant difference in mean of Lexington, Kentucky and Richmond, Kentucky Alternative Hypothesis: There is a statistically significant difference in mean of Lexington, Kentucky and Richmond, Kentucky.

Test statistic under Ho for unequal variances This value is less than -1.706 (the 5% upper level of distribution), therefore we have sufficient evidence to reject Ho and accept the alternative hypothesis. The p-value is less than alpha of 5%. Question 5 Null Hypothesis: career choice and race appear independent Alternative Hypothesis: career choice and race do not appear independent Confidence 95 alpha 0.05 p value 0.007865624 r 6 c 4 df 15 Based on the results above, our obtained p-value of 0.

007866 is less than our alpha of 0.05 (5%), therefore we do not have sufficient evidence to support the null hypothesis. Career choice and race appears not to be independent. (Workings are on the excel file attached) Question 6 (a)   Coefficients Intercept 13444.60858 X Variable 1 2924.796996 (b)   Coefficients Intercept 39058.31372 X Variable 1 0.440966035 (c)   Coefficients Intercept 11739.20357 X Variable 1 0.150709827 X Variable 2 2582.845062 (a) (b) [c] Multiple R 0.871055435 Multiple R 0.

59009967 Multiple R 0.888279782 R Square 0.758737571 R Square 0.34821762 R Square 0.78904097 The best model is model 3. , the model has R square of 0.78904097 which is much higher than the other two model. With R approaching one, it shows a better correlation between income and the other two variables. A better parent’s income, the better and longer the duration of education and this increases the income (Mukhopadhyay 67). References Mukhopadhyay, Nitis. Probability and Statistical Inference.

Boca Raton, Fla: CRC, 2011. Print.