Lab01 Assignment Name on back only

Directions: Complete the following exercises. You may work together with other students, but write up your own answers. The names of those you worked with must appear on this sheet.

1. Use the serum creatine phosphokinase data of exercise 2.50 (page 49) to answer the following. (If you had difficulty loading this data from the CD that came with your book, you can find it on our class web page.

(a) Does the histogram of these 36 data points support the claim that indeed serum creatine phosphokinase data of this sort follows the normal (bell shaped) curve? _________ Why/why not?

(b) Use Minitab to make a stemplot and a boxplot. Sketch them here.

Use the given descriptive statistics to

(c) determine the interquartile range (IQR = Q3 – Q1) _________,

(d) to give the standard deviation (labeled “StDev”) __________, and

(e) to give the standard error of the mean (labeled “SE Mean”) __________.

(f) Incidentally, what is the relationship between the standard deviation and the standard error of the mean for these data? (See the discussion of this in Section 6.2 on pages 180-181.)

2. Use the moth count data (2400, 6500, 320, 2700, 80, 230, 490, 13000, 1200, 300) to answer the following.

(a) Obtain the relevant graphs and verify that the data have a large right tail. For these data, provide

the average __________ and

standard deviation ___________ of the moth counts.

Find the five number summary: _________ _________ _________ _________ _________

(b) (Read about transformations in my Introduction to Minitab note before completing this part.) Verify that the skew of the transformed log-count data is less than for the original data, and that the log-counts do appear to come from a normal distribution. For these log-count data, provide

the average (mean) __________
and standard deviation _______________.

(c) Report the following:

the log of the average of the counts ____________

the average of the log’s of the counts? ___________. Are these two equal? _____

the log of the standard deviation of the counts ____________

the standard deviation of the log’s of the counts? _______. Are these two equal?______

3. The center, spread and shape of the sampling distribution of the mean using the exponential distribution as population. The population mean is \mu = 3.0 and the population standard deviation is \sigma = 3.0. Note that the population is extremely skewed to the right.

(a) Obtain a histogram of the means of samples of size n = 4 (stored in columns c1 – c4, and put the row means in the column c5 – the data is tending toward a bell-shape (normal) yet still quite

skewed – in which direction? _________ Estimate the mean ________ and SD _________ of this distribution, and compare these to \mu = 3.0 and \sigma=3.0

(b) Repeat the process as in (a) but for samples of size n = 9 (stored in columns c1 – c9, and put the row means in the column c10).

Do the sample means still have a skew? ______ . Estimate the mean ________ and SD _________,
and compare these to \mu = 3.0 and \sigma = 3.0.

(c) Repeat the same process but for samples of size n = 16 (stored in columns c1 – c16 and with the row means saved in column c17).

What about the skew? ______________. Estimate the mean ________ and SD _________ of this distribution, and compare these to \mu = 3.0 and \sigma = 3.0.

(d) Finally, repeat the same process but for samples of size n = 25 (stored in columns c1 – c24 and with the row means saved in column c25). Verify that the

skew is almost gone, and finally estimate the mean ________ and SD _________ of this distribution, and compare these to \mu = 3.0 and \sigma = 3.0.