You must SHOW ALL WORK for full credit (except for plots and things computed entirely in R, in which case just state "from R"). Please staple your assignment if it is more than one page.

Where the problem asks you to create a graph, you should do one of the three following things: (a) if you are using a word processor, include the graph in the document file directly, (b) print the graph out separately, then cut off the white space with scissors and tape it into your homework in the appropriate place, or (c) include the graphs as figures on separate pages, labeling each graph clearly, and referring to the labels in the text of your homework. In any case, do not turn in transcripts of your computer sessions. Include only the most relevant output, circling or highlighting if necessary, and don't make the grader fish for the answer. These instructions also apply for all future assignments, even if they are not repeated on those assignments.

Required problems:

1) IQ scores are normally distributed with a mean of 100 points and a standard deviation of 15 points.
  a) A group of 49 people is selected at random. Find the probability that their mean IQ score is at least 105.
  b) A group of 20 people is selected at random. Find the probability that their mean IQ score is between 105 and 110.
2) Problem 4.6 parts(a)-(c) plus revised parts(d) and (e): The data in the file webaccess represent the length of time (in seconds) between accesses of a particular web page on the internet (use the R command "scan" to read in the data instead of "read.table" since there is only variable).
  a) Construct a stem and leaf diagram for the data.
  b) Construct a boxplot.
  c) Construct a histogram.
  d) Construct a normal probability plot.
  e) Describe this distribution (central location, spread, shape, and outliers).
3) Problem 6.2 parts(a)-(c): In a continuous chemical process, data is kept on the purity of a solvent recycle stream. Historically the purity is approximately normally distributed with mean 97 and (population) standard deviation 0.20. The plant had to switch suppliers of filters used in the recycle stream due to delivery problems with the old supplier. Production management was concerned whether use of the new filters would reduce the purity of the recycled solvent. After the change in filters, 10 hourly assays of the solvent purity resulted in the data in the file purity.
  a) State the null and alternative hypotheses to test the production management's concern.
  b) Using a significance level of alpha=.05, define the test statistic and rejection region.
  c) Calculate the test statistic and draw a conclusion. (You can do this by hand or use the R command t.test with an appropriate value for the mu parameter.)
4) Problem 6.3 (parts c-e modified): An investigation was conducted on a lathe to determine if the spindle speed affected the surface finish along the path of the cutting tool. Sixteen material blanks were cut, half at a low spindle speed of 500 RPM and half at a high spindle speed of 1060 RPM. The order of the cutting speed was randomized. The surface finish for each piece cut was measured on a profilometer, and the square roots of the surface finish measurements are in the file spindle (use these as your data)
  a) Make comparative boxplots of the two sets of data (if you read in the dataset using read.table, then you can just use the boxplot command on the dataset object).
  b) Calculate means and standard deviations for each set of data.
  c) Test for equality using a pooled t-test (assuming equal variances) (in R, you can use t.test(x,y,var.equal=T) where x and y are the two datasets).
  d) Since the two variances don't really look equal, try a two-sample t-test not assuming equal variances (in R, use t.test(x,y) replacing x and y with the appropriate names).
  e) What confidence do you have that RPM affected surface finish? Does it matter if you assume that the variances are equal?
5) The prices of medications prescribed to both humans and animals may differ. The file medication gives the price in dollars for one dose of each of eight medications for humans and animals. Conduct a paired t-test to see if humans and animals are charged different amounts for the same drugs.
6) Thoughts on the final project.
  a) Do you have a general topic in mind for the final project?
  b) If so, do you have a specific idea or are you hoping that the professor will find a project in that area? If you have an idea, please explain very briefly (more details later).