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Zingaro stone printing is a company that specializes in printing images or patterns on polished or unpolished stones.

INSTRUCTIONS TO CANDIDATES
ANSWER ALL QUESTIONS

Advanced Statistics - Python

1. Business Report:  Submit answers to all the questions in a sequential manner. Your report must include a detailed explanation of the approach taken, inferences, and insights. Include outputs such as graphs, tables, and all other relevant information. Business Report must not include any codes. You will be evaluated based on Business Report only. Hence please ensure that your Business Report is logical and detailed enough (without any code) for a reader somewhat conversant in analytics to understand the solution mechanism. 

2. Jupyter Notebook File: This is a must and will be used for reference while evaluating

Problem 1:

 Zingaro stone printing is a company that specializes in printing images or patterns on polished or unpolished stones. However, for the optimum level of printing of the image the stone surface has to have a Brinell's hardness index of at least 150. Recently, Zingaro has received a batch of polished and unpolished stones from its clients. Use the data provided to answer the following (assuming a 5% significance level);

 

1.1 Earlier experience of Zingaro with this particular client is favorable as the stone surface was found to be of adequate hardness. However, Zingaro has reason to believe now that the unpolished stones may not be suitable for printing. Do you think Zingaro is justified in thinking so?

1.2 Is the mean hardness of the polished and unpolished stones the same?

 

Dataset - Link

 

Problem 2:

 

Aquarius health club, one of the largest and most popular cross-fit gyms in the country has been advertising a rigorous program for body conditioning. The program is considered successful if the candidate is able to do more than 5 push-ups, as compared to when he/she enrolled in the program. Using the sample data provided can you conclude whether the program is successful? (Consider the level of Significance as 5%)

Note that this is a problem of the paired-t-test. Since the claim is that the training will make a difference of more than 5, the null and alternative hypotheses must be formed accordingly.

 

Dataset - Link

 

Problem 3:

 

Dental implant data: The hardness of metal implant in dental cavities depends on multiple factors, such as the method of implant, the temperature at which the metal is treated, the alloy used as well as, on the dentists who may favour one method above another and may work better in his/her favourite method. The response is the variable of interest.

 

3.1 Test whether there is any difference among the dentists on the implant hardness. State the null and alternative hypotheses. Note that both types of alloys cannot be considered together. You must state the null and alternative hypotheses separately for the two types of alloys.?

3.2 Before the hypotheses may be tested, state the required assumptions. Are the assumptions fulfilled? Comment separately on both alloy types.? 

3.3 Irrespective of your conclusion in 2, we will continue with the testing procedure. What do you conclude regarding whether implant hardness depends on dentists? Clearly state your conclusion. If the null hypothesis is rejected, is it possible to identify which pairs of dentists differ?

3.4 Now test whether there is any difference among the methods on the hardness of dental implant, separately for the two types of alloys. What are your conclusions? If the null hypothesis is rejected, is it possible to identify which pairs of methods differ?

3.5 Now test whether there is any difference among the temperature levels on the hardness of dental implant, separately for the two types of alloys. What are your conclusions? If the null hypothesis is rejected, is it possible to identify which levels of temperatures differ?

3.6 Consider the interaction effect of dentist and method and comment on the interaction plot, separately for the two types of alloys?

3.7 Now consider the effect of both factors, dentist, and method, separately on each alloy. What do you conclude? Is it possible to identify which dentists are different, which methods are different, and which interaction levels are different?

 

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