QUESTION NO.4

French Biscuit Manufacturer (FBM), produces two types of biscuits (i) double chocolate biscuits and (ii) tea time biscuits in two separate manufacturing units. They are interested in expanding the manufacturing units (one by one) because there is a demand in the market but facing a difficulty to decide which manufacturing unit should expand first. Company officials decided that the expansion decision was based upon monthly demand.

FBM official consults you and requests to give your valuable suggestion which will be helpful for final decision. you analyzed the following normally distributed data:

	Monthly Sale of Biscuits
Double Chocolate	8551	6314	5259	8138	8429	4807	8025	6845	6478	7513
	9125	4894	9106	8775	10070	7845	6229	8459	10542	4196
Tea Time	10247	6601	7404	8919	9255	8404	6304	7803	11474	9131
	13345	8118	6713	7439	10957	12098	9134	7535	10316	8125

Kindly provide the following information regarding your data analysis.

a. Write the null and alternative hypothesis.

b. Determine the calculated value of the test statistic with equal variances assumption.

c. Calculate the tabulated value (critical value) of the test statistic at 0.05 level of significance.

d. Develop a 95% confidence interval for the difference between the average sales of the two types of biscuits assuming that the variances are equal.

e. On average, sales of double chocolate biscuit is 500 units more than tea time biscuits. Comments in the light of part d result.

With reference to question # 4, perform the analysis for the verification of the assumption and answer the questions given below:

1. Write the name of statistical technique used for analysis
2. For the comparing the two variances, statisticianstudy ratio of two variances while when comparing the two means, study the difference of two mean. Give the logical reason, why we study the ratio of two variances and why not the difference of two variances.
3. Write the calculated value of test statistics
4. Write the two tabulated value of test statistics.
5. Comments about the assumption taken in question # 4, in the light of your analysis.