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We will explore 95% confidence interval estimation of a population mean  using the t- confidence interval asdiscussed in Section 11.2 of the text.I. You will be asked to generate 10 random samples of size n = 5 from a skewed distribution and use Minitab tocalculate the t-interval estimate of  based on each of the ten random samples. You will then count the number ofintervals that cover . Also, you will be asked to plot five of the intervals. II. You will then be directed toconduct a comprehensive study that determines the coverage percentage for 1,000 95% t-interval estimates for eachof three situations:[A] Population with a normal distribution and sample size n = 5[B] Population with a skewed distribution and sample size n = 5[C] Population with a skewed distribution and sample size n = 50.The t-interval is designed to have a specified coverage probability for  when based on random samples of sizen > 1 drawn from a normal distribution. Thus, in [A] with n = 5, you should find that about 950 of the 1,000t-intervals cover , that is, the t-interval methodology delivers nearly the advertised 95% coverage rate forsampling from the normal distribution. In other words, in repeated applications of the method, about 95% of theconfidence intervals will contain the value of the parameter of interest. However, the t-interval may have muchless coverage probability than advertised when it is based on random samples drawn from a skewed distribution.In fact, there may be a considerable diminution in coverage probability if n is small. Thus, in [B] with n = 5,you should find that the t-interval delivers much less than the advertised 95% coverage rate. This weakness issomewhat eliminated if the sample size is large. Thus, in [C] with n = 50, you should find that the t-intervaldelivers nearly the advertised 95% coverage rate.Use File > Open Worksheet to load u:msucoursestt201sLabci.mtw into your computer. Column X formsa nearly normal distribution. Column Y forms a skewed distribution.Use Graph >Dotplot with option ‘Multiple Y’s simple’, select X and Y as variables to graph. Describe theshapes of the distributions X and Y.1. Distribution of X: close to a bell / skewed to the right / skewed to the left / uniform / u-shaped.2. Distribution of Y: close to a bell / skewed to the right / skewed to the left / uniform / u-shaped.Use Stat > Basic Statistics > Display > Descriptive Statistics to get the mean of each distribution and record them:3. X = mean(X) = _____________4. Y = mean(Y) = ______________.In preparation for constructing the t-intervals with sample sizes n = 5 and n = 50, we need the values of themultipliers t* (also called confidence factors) for 95% confidence intervals. To find them using Table A.2 fromthe textbook, you need to use the confidence level, 95% in this case, and the degrees of freedom=n-1. Whenfinding the t* multipliers using Minitab, you need to input the amount in left tail (cumulative probability) of.975 for Minitab to output the t* multiplier. Use Calc > Probability Distributions > T, select Inversecumulative probability option. Leave the non-centrality parameter equal to 0. Enter 4 as degrees of freedomand Input constant .975.5. The value of the t* multiplier for 95% confidence and 4 degrees of freedom is t*=_______.Use the same menu again with 49 degrees of freedom to get the t multiplier (confidence factor) for 49 df.6. The value of the t* multiplier for 95% confidence and 49 degrees of freedom is t*=____________.These values will be used in calculating some of the confidence intervals as required below.I. In this section you will be asked to generate 10 random samples of size n = 5 from the skewed Y distributionand use Minitab to calculate the confidence interval estimate of Y based on each of the 10 random samples.You will be asked to count and report the number of intervals that cover Y. Also, you will be asked to plot fiveof the intervals.Use Calc > Random Data > Discrete to generate 5 rows of data, store them in columns C21-C30. Selectsamples from the skewed population Y, probabilities are in Y_probs. Each column of data is a random sampleof size n = 5 from the Y distribution. Look at these columns to see the data in the ten samples of size n = 5.Use Stat > Basic Statistics > 1-Sample t to calculate the 95% confidence intervals based on the samples incolumns C21-C30. Do not check the box “ Perform hypothesis test”. To check that the confidence level is setat 95%, click on options and make sure the confidence level is 95%. The field ‘Alternative’ should remain ‘notequal’ (do not change it). Press OK and again OK. Your ten intervals should appear on your screen.7. For how many of the 10 intervals does the sample meanyequal the population mean Y = 9.9849 exactly(not approximately)? ____________ (Hint: we don’t expect this to happen often.)8. How many of the 10 intervals cover the population mean Y = 9.9849, the value that you recorded in question4? In other words, for how many of the 10 intervals does the population mean Y = 9.9849 fall between the leftand right end points (lower and upper bounds) of the confidence interval? _______ (Of course, each intervalcovers the sample mean which is the center of the interval; you must see how many cover the population mean.)Use the number lines below to plot your first five intervals: on each line. Do this by marking the endpoints ofthe intervals using left parenthesis “(“ for the lower end and right parenthesis “)” for the upper end._____________________________________________________________________________ C21 7.0 8.0 9.0  11.0 12.0 13.0 14.0 Y_____________________________________________________________________________ C22 7.0 8.0 9.0  11.0 12.0 13.0 14.0 Y_____________________________________________________________________________ C23 7.0 8.0 9.0  11.0 12.0 13.0 14.0 Y_____________________________________________________________________________ C24 7.0 8.0 9.0  11.0 12.0 13.0 14.0 Y_____________________________________________________________________________ C25 7.0 8.0 9.0  11.0 12.0 13.0 14.0 YLook on your screen for the C21 (first) t-interval. You are now to verify that Minitab is giving the same resultas comes from the formula in the textbook, page 422, that is, fromnsy  t *. For your sample C21, thescreen shows9. Sample mean=y  ________10. Sample standard deviation =s _________.11. Sample size n = ______12. For 4 degrees of freedom, the multiplier t*=_______ (see t* calculated by Minitab, question 5).13. Calculate the lower endpoint of the intervalnsy  t *= _________14. Calculate the upper endpoint of the intervalnsy  t *= _________ .Do these calculations agree with your Minitab interval C21 that appears on your screen? _______II. You will now be directed to conduct a comprehensive study to determine the coverage percentage for 1,000interval estimates for each of three situations:[A] Population X (a normal distribution), sample size n = 5[B] Population Y (a skewed distribution), sample size n = 5[C] Population Y (a skewed distribution), sample size n = 50Following the directions below will place the 1,000 samples of size n into rows; this is convenient for doingthese parts.[A]Use Calc > Random Data > Discrete to generate 1,000 rows of data, store them in store the results in columnsC11-C15. Select samples from the normal population X, probabilities are in X_probs. Here each of the 1,000rows is a random sample of n = 5 from X, with the sample values in the five columns C11-C15.Use Calc > Row Statistics with option “mean” checked. Input variables are C11-C15. Store the means in thecolumn SamMean. This will place 1,000 sample means into the Column SamMean.Then use Calc > Row Statistics with option “standard deviation” checked and Input variables C11-C15, andstore the sample standard deviations in the Column SamStdev.Use Calc > Calculator to calculate the lower confidence limit: store the result in variable LCL, expression:‘SamMean ‘ -2.7764  ‘SamStdev’/ 5.5 In Minitab’s programming language, ** indicates raising to a power(raising to a power of 0.5 is equivalent to taking a square root). There is a key in Minitab’s menu thatcorresponds to **. For the upper confidence limit, store the result in variable UCL, expression: ‘SamMean’ +2.7764  ‘SamStdev’/ 5.5.Use Calc > Calculator and the expression sum(LCL Random Data > Discrete to generate 1,000 rows of data, store them in columns C11-C15. Selectsample from the highly skewed population Y, probabilities are in Y_probs. You will overwrite the data alreadyin those columns. Here each of the 1,000 rows is a random sample of n = 5 from Y, with the sample values inthe five columns C11-C15.Use Calc > Row Statistics with option “mean” checked. Input variables are C11-C15. Store the means in thecolumn SamMean. This will place 1,000 sample means into the Column SamMean.Then use Calc > Row Statistics with option “standard deviation” checked and Input variables C11-C15, andstore the sample standard deviations in the Column SamStdev.Use Calc > Calculator to calculate the lower confidence limit column LCL, expression :’SamMean’ - 2.7764 ‘SamStdev’/ 5.5 and the upper confidence limit column UCL, expression: ‘SamMean’ + 2.7764 ‘SamStdev’/ 5.5.Use Calc > Calculator and the expression sum(LCL Random Data > Discrete to generate 1,000 rows of data, store them in columns C11-C60. Selectsamples from the highly skewed population Y, probabilities in Y_probs. Here each of the 1,000 rows is arandom sample of n = 50 from Y, with the sample values in the fifty columns C11-C60.Use Calc > Row Statistics with option “mean” checked. Input variables are C11-C60. Store the means in thecolumn SamMean. This will place 1,000 sample means into the Column SamMean.Then use Calc > Row Statistics with option “standard deviation” checked and Input variables C11-C60, andstore the sample standard deviations in the Column SamStdev.Use Calc > Calculator to calculate the lower confidence limit Column LCL, expression: ‘SamMean’ -2.0096 ‘SamStdev’/ 50.5 and the upper confidence limit Column UCL, expression: ‘SamMean’ + 2.0096 ‘SamStdev’/ 50.5.Use Calc > Calculator and the expression sum(LCL