BIOSTAT 335                       Lab4: Second Computer Assignment                      Name __________________________

 

Directions:  Do not print out computer output – just copy whatever you need from the computer screen onto this page.   .  You are encouraged to work together with other students, but write up your own answers. 

 

  1. Take five samples of size 8 from a normal population with mean =100, SD = 16.  Recall that to generate 5 samples of size 8 from this population by clicking Calc->Random Data->Normal; after “Generate” type “5” to get 5 rows of data (each one is a sample); after “Store in Column(s),” type “c1-c8”; Type “100” after “Mean and “16” after “StDev” then hit “OK.”  This is a simulation of taking 5 random samples of 8 people from the general population and then measuring their IQ’s.  For each sample, look at the histogram (Graph->Histogram ) and do a normal probability plot.  You have to transpose the 5 samples to columns first.  Use the” Manip->TransposeColumns” function.  With Minitab, before doing a normal probability plot, you have to convert scores to standard units (Calc->Standardize; store in columns C8-C12); and then Graph->ProbabilityPlot for each of C8 to C12..

 

  1. Repeat this for three samples of size 25.  Then for three samples of size 36.

Explain what you observe. 





  1. In a certain human population, 30% of the people have “superior” vision (that is, they score 20/15 or better on a standardized vision test).  We first generate 1000 samples of size k = 5 from such a population.  Store each sample in a row, using column c1-c5. (A dichotomous population is said to be Bernoulli Population.  So, use Calc->RandomData->Bernoulli, with a probability of success of .30.    

 

(a)     Obtain a histogram of the sample proportions.  Put the sample proportions in row C7.  Look at the histogram and a normal probability plot of the row proportions.   Don’t forget to standardize the row proportions.   Estimate the mean ________ and SD _________ of this distribution.  How do these estimated compare with the true values.

 

(b)     Repeat the same process but for samples of size k = 10. Estimate the mean ________ and SD _________ of this distribution.  How do these estimated compare with the true values.

 

(c)     Finally, repeat the same process but for samples of size k =  20  Again estimate the mean ________ and SD _________ of this distribution.  Write what you have observed in this exercise. How do these estimated compare with the true values.




 

(d)     Now take one sample of size 100.  Compute the sample proportion.  Compare the sample proportion to the population proportion.  Your sampling error is ________________.  The standard error for this experiment is _________.   How large of a sample is needed for the standard error to be half this size? ____________

  1.  Use the serum creatine phosphokinase data of exercise 2.38 (page 59) to answer the following.

 

(a)     Make a histogram and a normal probability plot.  

 

(b)     Use your observations from part 1 above to answer the following question.  Does the histogram and normal probability plot of these 36 data points support the claim that indeed serum creatine phosphokinase data of this sort follows the normal curve? _______  Why/why not?

 

 

(c)     Use the “Basic Statistics” display (such as “Mean”, “StDev” and “SE Mean”) to answer the following:  Your best guess for the true average serum CK level μ of all healthy men is  __________.  Your best guess for the accuracy of your estimate is ±______________. Now include both to give your conclusion μ =  _________±______________.  If you measured the serum CK level of a 37th man, the reading would be about __________, give or take _____, or so.  If you took another sample of 36 men, the average serum CK level of these 36 men would be about ____________, give or take ___________, or so.  What is the relationship between the standard deviation and the standard error of the mean for these data?

 

 

5.  This last exercise does not involve Minitab.  The Damen Hall elevator is certified to hold 16 persons, with a maximum load limit of 2500 pounds.  Suppose that the weights of Loyolans (with coats, books, etc) follow the normal curve with a mean weight of 150 lbs and SD = 25 lbs. (Does this make sense?  What doe the 68% and 95% rules say?).  Suppose that you observe 16 persons in the Damen Hall elevator.   The total weight of the 16 persons will be about ____________ lbs, give or take __________ lbs, or so, and will follow the _____________ curve.  What is the chance that 16 persons overload the Damen Hall elevator?  _______________________.