Deep fungal infections include all except:

This oral lesion seen in primary syphilis is called a chancre.

Question:  You work for a medical device company, and your product is battery packs for artificial hearts.  The heart will last almost indefinitely once implanted, but it needs the batteries charged in order to work.  The current battery pack is believed to have a mean of 240 minutes with a population standard deviation of 50 minutes.  Your company has developed a new battery pack which it hopes will last longer.  You take a sample of 8  of the new battery packs and test their life spans.  You find them to have a mean life of 270 minutes.  You want to run a statistical test to determine if the battery life has increased with the new technology.  State the null and alternative hypotheses, and any other assumptions you need to make. What is the p-value for your sample? Using the alpha = 0.05 level of significance, what is your conclusion?  In addition to stating “reject/do not reject the null hypothesis,” please put it in plain English.  What does your conclusion mean for the life of the new technology battery packs?

We measure the viscosity of a particular fluid by putting the fluid in a calibrated tube, and then dropping a small ball into the tube.  X is the random variable which denotes how many seconds it takes for the ball to drop to the bottom of the tube.  The longer the drop, the more viscous the fluid.   Below is a histogram of your latest 15 trials. MidTerm_QuestionL_Chart_A.png Your team wants to consider those 15 trials to be one batch, and notes that the average dropping time is 1.38 seconds for the batch shown.  It also assumes the standard deviation for the population of all dropped balls through this tube with this fluid is assumed to be 1.25 seconds.   Your company is advertising the average dropping time as 2 seconds, and this is assumed to be the population average.  For this product, more viscous (longer dropping times) is better. Your team member says, “Hey, I think we can use the Central Limit Theorem here even though this histogram doesn’t even look remotely normally distributed.  Let’s take 3 more batches, so we will have a total of 4 batches of 15 ball drops.  That’s 60 balls total.  Then the distribution of the sample means for batch 1, batch 2, batch 3, and batch 4 will be normally distributed, with a mean and standard deviation we can measure.  That will tell us what we really want to know:  if our product really does have a mean of 2 and a stdev of 1.25, what are the chances that a random sample like the one we took will give those results?” Is your team member correct?  If so, apply the Central Limit Theorem and tell me the results.  If not, tell me why not and what, if any, changes could be made to get the information the team wants.  (Note: this is specifically a question on the Central Limit Theorem, not on hypothesis testing.  Please don’t formulate or test any hypotheses here.  Just discuss the Central Limit Theorem.)

You have a completely randomized design of four treatments for your grocery bag manufacturing.  You want to improve the tensile strength of the bags, and your engineers think the tensile strength can be a function of the hardwood concentration in the pulp.  Higher tensile strength is better. A team of engineers is investigating four levels of hardwood in the pulp, cleverly called Levels A, B, C, and D. You’ve run the ANOVA below in Excel on data taken from a fully randomized experiment.  The numbers refer to tensile strength. What is your analysis of the results?  In particular, does the treatment make a statistically significant difference, and if so, which treatment(s) are better or worse?  If you can, list them in order from best to worst.  If you can’t, tell me why you can’t.  Test at alpha = 0.05. Anova: Single Factor SUMMARY         Groups Count Sum Average Variance A 7 89 12.71 3.24 B 7 126 18.00 0.67 C 7 94 13.43 2.29 D 7 70 10.00 1.00 ANOVA             Source of Variation SS Df MS F P-value F crit Between Groups 231.8214286 3 77.27380952 42.98675497 8.30 E-10 3.00878657 Within Groups 43.14285714 24 1.797619048                     Total 274.9642857 27

Below is a screenshot of an Excel regression.  We will refer to this as “Screenshot A1” in future questions.   You will need this for the question below.  Please choose “true” to indicate you can view the graphics. Problem A graphics.png

Which of the following is a type of Granulocytes?

Which spleen areas are responsible for the destructing old RBCs?

For a healthy person, what are the most abundant white blood cells?

What is considered a member of the primary lymphoid organs?