Version A Problem 1/Version B Problem 3:Version A: Assume X1,…,X25 iid ˆ¼ N(1,σ2). (a) [5

Version A Problem 1/Version B Problem 3:Version A: Assume X1,…,X25 iid ˆ¼ N(1,σ2). (a) [5 pts] The MLE of σ2 isˆ σ2 =P25 i=1(Xi ˆ’1)2 25)Show that 25ˆ σ2/σ2 has a Chi-squared distribution with 25 degrees of freedom. (b) [5 pts] Use the result in part (a) to derive a 99% confidence interval for σ2) (Your quantiles should have numerical valuesnot just symbols.) Your final answer should be in interval form (L,U), for some lower bound L and upper bound U.  Version B: Assume X1,…,X15 iid ˆ¼ N(1,σ2). (a) [5 pts] The MLE of σ2 isˆ σ2 =P15 i=1(Xi ˆ’1)2 15)Show that 15ˆ σ2/σ2 has a Chi-squared distribution with 15 degrees of freedom. (b) [5 pts] Use the result in part (a) to derive a 90% confidence interval for σ2) (Your quantiles should have numerical valuesnot just symbols.) Your final answer should be in interval form (L,U), for some lower bound L and upper bound U.  Version A Problem 2/Version B Problem 4:Version A: Edgar Anderson collected data on sepal widths (in centimeters) of the Setosa species of iris flower (Bulletin for the America Iris Society, 59, 2-5, 1935). For a random sample of 18 flowers, the sample mean sepal width was 3)228 cm with a sample standard deviation of 0.329) A normal quantile-quantile plot of the sample widths is below.-2 -1 0 1 22)42)62)83)03)23)43)6Normal Q-Q PlotTheoretical QuantilesSample QuantilesUsing a significance level of .05, conduct a one-sample t-test to determine if the mean sepal width in the population of Setosa species of iris flowers diï¬ers from 3)2 cm:(a) [2 pts] State hypotheses in terms of the population parameter. (Define any symbols used.) (b) [3 pts] Check assumptions and calculate the test statistic. (c) [2 pts] Find the p-value. State which distribution table you used and where you looked on the table to find the p-value. (d) [1 pt] State your decision (Reject H0 or Fail to reject H0). (e) [2 pts] Provide a conclusion in terms of the research study.  Version B: Edgar Anderson collected data on sepal widths (in centimeters) of the Virginica species of iris flower (Bulletin for the America Iris Society, 59, 2-5, 1935). For a random sample of 18 flowers, the sample mean sepal width was 2)994 cm with a sample standard deviation of 0.372) A normal quantile-quantile plot of the sample widths is below.-2 -1 0 1 22)62)83)03)23)43)63)8Normal Q-Q PlotTheoretical QuantilesSample QuantilesUsing a significance level of .05, conduct a one-sample t-test to determine if the mean sepal width in the population of Virginica species of iris flowers diï¬ers from 2)9 cm:4(a) [2 pts] State hypotheses in terms of the population parameter. (Define any symbols used.)(b) [3 pts] Check assumptions and calculate the test statistic. (c) [2 pts] Find the p-value. State which distribution table you used and where you looked on the table to find the p-value.(d) [1 pt] State your decision (Reject H0 or Fail to reject H0). (e) [2 pts] Provide a conclusion in terms of the research study.