# STATISTICS ASSIGNMENT Essay Example

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In order to test that whether there is significant difference in terms of the coffee quality and the service quality we have applied the independent sample t test assuming equal variances. The null and the alternative hypothesis are as follows:

Ho: There is no difference between the service quality and the coffee quality.

H1: There is significant difference between the service quality and the coffee quality.

The results of the one sample t test are shown below:

 t-Test: Two-Sample Assuming Equal Variances Variance Observations Pooled Variance Hypothesized Mean Difference 0 P(T<=t) one-tail t Critical one-tail P(T<=t) two-tail t Critical two-tail

As we can see that the one tail and the two tail p values are higher than the level of significance of 0.05, therefore, we accept the null hypothesis and we conclude that there is insignificant or no difference between the service quality and the coffee quality between the outlets.

The answers to all the questions are as follows:

The prediction regarding the mix proportions does not hold for January as the average mixture comprises of 26.16% Expresso, 17.36% Mocha and 56.48% Sublime rather than required 30% Expresso, 10% Mocha and 60% Sublime.

The prediction regarding the mix proportions does not hold for December as the average mixture comprises of 37.35% Expresso, 27.74% Mocha and 34.91% Sublime rather than required 30% Expresso, 10% Mocha and 60% Sublime.

We have applied independent sample t tests for each of the three supplies separately. The results of the tests are shown in the table below.

 t-Test: Two-Sample Assuming Equal Variances Espresso Espresso 0.261646042 0.373481918 Variance 0.013904615 0.02910687 Observations Pooled Variance 0.021505742 Hypothesized Mean Difference 0 -2.223378427 P(T<=t) one-tail 0.016687404 t Critical one-tail 1.693888703 P(T<=t) two-tail 0.033374808 t Critical two-tail 2.036933334
 t-Test: Two-Sample Assuming Equal Variances 0.17359136 0.277373689 Variance 0.005885037 0.019006128 Observations Pooled Variance 0.012445582 Hypothesized Mean Difference 0 -2.712222196 P(T<=t) one-tail 0.005332 t Critical one-tail 1.693888703 P(T<=t) two-tail 0.010664 t Critical two-tail 2.036933334
 t-Test: Two-Sample Assuming Equal Variances 0.564762599 0.349144393 Variance 0.011659773 0.041684323 Observations Pooled Variance 0.026672048 Hypothesized Mean Difference 0 3.849166605 P(T<=t) one-tail 0.000267005 t Critical one-tail 1.693888703 P(T<=t) two-tail 0.00053401 t Critical two-tail 2.036933334

Since, the one tail and two tail p values of the three supplies is less than 0.05 level of significance therefore, we conclude that there has been a significant change in the portions of the three types of bean between January and December[ CITATION Mar10 l 3081 ].

Based on the December data the new expected market mix is show in exhibit 4 in the appendix. The moving average technique has been used to compute the expected market mix. These are shown in the table below:

## New expected market mix

 Espresso Espresso Average Proportions