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. Write the null and alternative hypothesis. Determine the calculated value of the test statistic with equal variances assumption. Calculate the tabulated value (critical value) of the test statistic at 0.05 level of significance.
Question # 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
|
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.
- Write the null and alternative hypothesis.
- Determine the calculated value of the test statistic with equal variances assumption.
- Calculate the tabulated value (critical value) of the test statistic at 0.05 level of significance.
- Develop a 95% confidence interval for the difference between the average sales of the two types of biscuits assuming that the variances are equal.
- “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:
- Write the name of statistical technique used for analysis
- “For the comparing the two variances, statistician study 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.
- Write the calculated value of test statistics
- Write the two tabulated value of test statistics.
- Comments about the assumption taken in question # 4, in the light of your analysis.
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