[Solved] ISE 390-Minitab Assignment 2

1.a.

Calculate>Random Data

Let the number of data points be 30.

Minitab wont pick up the column automatically, so youll have to manually type in c1 under Store in Column(s). Later rename that column as Sample Data. Select Normal because we want our sample data to be normally distributed.

Enter the value of the Mean and Standard Deviation from Minitab Assignment 1. This will let each of you create data sets sampled from different normal distributions. None of you will have the same normal distribution.

1.b.

In order to do this, you will first need the values for Q1, Q2 and Q3 from your normally distributed sample data set.

Stat> Basic Statistics> Display descriptive Statistics

Select your sample data.

Click on Statistics and untick all boxes except First Quartile, Median and Third Quartile.

This will give you the three quartiles you need for this question.

Calculate >Probability Distribution > Cumulative Probability Distribution (CDF) Remember to enter the same mean and standard deviation as you used in 1a. Let the form of input be a single value.

Calculate the following probabilities

P (X<= First Quartile, Q1)

P (X<=Second Quartile, Q2)

P (X<= Third Quartile, Q3)

Enter these values of Q1, Q2 and Q3 sequentially under value to find each of the three probabilities associated with Q1, Q2 and Q3.

Ideally these probabilities should come out to be 0.25, 0.50 and 0.75 which is not the case here. In a single line comment why the probabilities you calculated are not 0.25, 0.50 and 0.75.

• c.

Graph> Probability Distribution Plot>View probability

Let the distribution be normal because we have a normally distributed sample data set. Enter the same sample mean and standard deviation as you used in 1a.

Under Options select Specified X value and left tail. Remember cumulative probabilities are always left tailed.

Enter the values of Q1, Q2 and Q3 sequentially under X value to find the cumulative probabilities associated with Q1, Q2 and Q3.

1.d.

Confidence interval on the mean

Stat>Basic Statistics> 1 sample T test/1 sample Z test

In a single line comment why a T test or a Z test is more appropriate here and why? (If a Z test is more appropriate, then use a 1 Sample Z test and if a T test is more appropriate, then use of 1 sample T test).

Select your sample data.

Click on Options. Let the confidence interval be 95% and then calculate the confidence interval on the mean.

Now change the confidence interval to 85% and recompute the confidence interval on the mean.

Did the length of the confidence interval change? In a single line comment on why it has increased or decreased.

1.e.

Normality Test

Graph>probability plot >simple

Select your sample data set which you want to test for normality. Under options menu let the confidence interval be 95%. Your criteria for accepting normality is 5% (0.05). If the P value given in the graph is greater than 5% (0.05) then your data is normally distributed.

In a single line comment whether the data is normally distributed or not.

2.a

Generate a sample data set of 50 points from a uniform distribution whose endpoints are same as given to you in Minitab Assignment 1. Re arrange the sample data from Minitab assignment 1 to find your endpoints.

2.b

Calculate the following probabilities

P (X<= First Quartile, Q1)

P (X<=Second Quartile, Q2)

P (X<= Third Quartile, Q3)

Ideally these probabilities should come out to be 0.25, 0.50 and 0.75 which is not the case here. In a single line comment why the probabilities you calculated are not 0.25, 0.50 and 0.75.

2.c

Graphically representation of cumulative probabilities.

Follow the same process as in 1.c but use uniform distribution instead of the normal.

2.d

Confidence interval on the mean.

Stat>Basic Statistics> 1 sample T test/1 sample Z test

In a single line comment why a T test or a Z test is more appropriate here and why? (If a Z test is more appropriate, then use a 1 Sample Z test and if a T test is more appropriate, then use of 1 sample T test).

Construct and contrast a 95% and 99% confidence interval on the mean. Did the length of the confidence interval change? In a single line comment on why it has increased or decreased.

Comment in a single line on why your method to construct confidence interval for this sample data set is wrong.

2.e

Normality Test

Check your sample data for normality at 95% confidence interval.

In a single line comment whether the data is normally distributed or not.