When a problem asks you to do a hypothesis test, follow the seven steps to success that we outlined on Tuesday. Show all graphs and information you used to determine your problems. When describing your data, make sure to do so completely.
Imagine you are turning these in to a governmental agency and are looking for money or have been hired to make a recommendation. Include everything necessary for someone to know your process AND what your recommendation of action would be.
Question One:
Hemoglobin counts are measured in grams per 100 milliliters of blood. For adult females, the population is relatively normal with an mu of 14 and sigma of 2.5.
A woman has been tested regularly for high levels of hemoglobin. Here are her results:
15 18 16 19 14 12 14 17 15 11
a) Give a 95% confidence interval for the patient's hemoglobin levels.
b) Do a hypothesis test, looking to see if the woman's level of hemoglobin could be considered high at the 90% level.
Question Two:
Hail damage. You work for an insurance company and are put in charge of determining rates for hail insurance--specifically wheat crops. Believe it or not, hail damage is a fairly large problem for crops--nationally, 11% of all wheat crops are destroyed by hail (I know, right?) You are going through some claims for a county in Colorado and get the following claims for percentage of destruction:
15, 8, 9, 11, 12, 20, 14, 11, 7, 10, 24, 20, 13, 9, 12, 5
Your job is to determine if there is more crop damage in this county than the normal average--if there is you are going to raise the rates for insurance for the following years. Assume at the national sd is 5%.
a) Give a 90% confidence level for hail damage in this county.
b) In order to validate your raising rates, you need to be 99% confident that the damage here is more than the national average. Should you raise your rates? Run a hypothesis test and explain completely.
Question Three:
In the United States, the mean yield of corn has been 120 bushels per acre. This year, 40 farmers gave their yields, with a mean of 123.8. The average yield has sd of 10 bushels.
a) Assume we want to prove that this sample shows the mean is different than average. Run a full hypothesis test, and give me the results.
b) Give a 99% CI for the yield of farmers.
Question Four:
Avalanches come in different types an styles, but a common one is a 'slab avalanche'. In Canada they have been extensively studied--they have a thickness in cm that is roughly N(67, 10.5). Scientists in Colorado are interested to see whether or not avalanches have similar characteristics to those in Canada--if they do, the research done in Canada can be used to explain certain snow phenomena in Colorado. If not, they will have to pay millions of dollars for their own research.
The scientists mark the thickness of the set of avalanches below:
59 51 76 38 65 54 49 62 68 55 64 67 63 74 65 79
a) Run specific hypothesis testing, and let the scientists know whether or not they can use the research from Canada.
Question Five:
Up until now, all of these questions have dealt with univariate data. This next one will challenge you........................
I have devised a method of teaching statistics in an hour I think is fantastic. I'm going to give a pre-test, teach, and then two weeks later give a post-test to see if students have learned anything.
here are two lists. The first is the pre-test, the second the post-test for the same person (for example, the 30 on the pre-test matches the 29 on the post-test).
Pre Test Pest Test
30 29
28 30
31 32
26 30
20 16
30 25
34 31
15 18
28 33
20 25
30 32
29 28
31 34
29 32
34 32
20 27
26 28
25 29
31 32
29 32
Set up a hypothesis test to see whether or not my program works. Assume that the standard deviation from pre to post test is 4.