# Mathematical Statistics I Assignment

All projects should be submitted in Excel or Word format. If you don't have access to either of these, then make use of Google Applications which is free by signing up with them. From there you can do all of the same work on as you can in an Excel Spreadsheet or a Word Document. You can also use Open Office or Libre/Open Office, but I do ask that you save it in .xls or .rtf rather than their native format.

1) Which of our the original questions in the above project data file have discrete data and which contain continuous data?

2) If we select 8 people from the dataset and then record whether they are a smoker or not, does this experiment a binomial one?, Why or why not?

3) If we choose three persons at random from our group of data. What is the probability that exactly two of them will be smokers?

4) Look at each of the columns of data in our project data file and by use of any methods in the text so far, determine which these columns appear to be normally distributed. Consider the histogram, the QQ plot, and the measures of central tendency to justify your results. Report on each of these five and make sure to include justification for your answers in the form of the graphs and/or calculations.

5) Look at the smoker column, and assume that the requirements for a binomial experiment exist each. Now, construct a 95% confidence interval for the proportion of this column.

6) Construct a 90% confidence a interval for the mean of one of the columns. We want to draw inference about the population mean by a random sample with replacement from the population. To see the effect of sample size on the inference, repeat the procedure three times using random samples of sizes 25, 40 and 64 respectively. Since for the purpose of this project one can also find out the population mean, you can see how well the sample mean estimates the population mean and whether the confidence intervals contain the actual population mean.

7) Construct a 90% confidence interval for the variance of one of the columns. We want to draw inference about the variance by a random sample with replacement from the population.

8) Remember to comment about every one of these items in your report. Itâ€™s important that you are able to tell what each of these tests means so the better I understand your work, the more I am convinced that YOU understand the material and I can grade appropriately.

1) Which of our the original questions in the above project data file have discrete data and which contain continuous data?

2) If we select 8 people from the dataset and then record whether they are a smoker or not, does this experiment a binomial one?, Why or why not?

3) If we choose three persons at random from our group of data. What is the probability that exactly two of them will be smokers?

4) Look at each of the columns of data in our project data file and by use of any methods in the text so far, determine which these columns appear to be normally distributed. Consider the histogram, the QQ plot, and the measures of central tendency to justify your results. Report on each of these five and make sure to include justification for your answers in the form of the graphs and/or calculations.

5) Look at the smoker column, and assume that the requirements for a binomial experiment exist each. Now, construct a 95% confidence interval for the proportion of this column.

6) Construct a 90% confidence a interval for the mean of one of the columns. We want to draw inference about the population mean by a random sample with replacement from the population. To see the effect of sample size on the inference, repeat the procedure three times using random samples of sizes 25, 40 and 64 respectively. Since for the purpose of this project one can also find out the population mean, you can see how well the sample mean estimates the population mean and whether the confidence intervals contain the actual population mean.

7) Construct a 90% confidence interval for the variance of one of the columns. We want to draw inference about the variance by a random sample with replacement from the population.

8) Remember to comment about every one of these items in your report. Itâ€™s important that you are able to tell what each of these tests means so the better I understand your work, the more I am convinced that YOU understand the material and I can grade appropriately.

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