# Project #22979 - Statistics Week 6 Assignment

State spreadsheet and book are attached.

Policy: When a claim is made and sample evidence seems to support the claim, we need to conduct a formal test to determine if the evidence is sufficient or significant. We call this type of test a hypothesis test. This week we will be conducting hypotheses tests about one population mean, hypotheses tests about one population proportion, and hypotheses tests for a population variance and/or standard deviation. (Recall that the variance is the square of the standard deviation.) Keep in mind that when testing a hypothesis, the sample evidence should support the claim; if it does not then there is no need to run a formal test. This week will also be testing claims about two population means involving two independent samples, claims about the population mean difference for two dependent samples, and claims about two population variances and/or standard deviations. The two sets of textbook exercises and the two activities should help you learn the material covered this week.

These two activities will help you determine if you grasped some of the key topics from our study of Chapters 8 and 9 and in that way it will help prepare you for answering some of the inference questions covered on Quiz #3 as well as the final exam project assessment. Furthermore, these activities meet the course outcome to select and apply the statistical test or tests that are most appropriate to analyze a data set.

In order to earn the full ten points for each of the two activites (a-j are each worth two points), your responses to these activities must be complete and reasonable.  An incomplete response would be one that does not answer all parts or the computations for a part or parts are not completed.  An example of an unreasonable response would be one in which what you write for Ho and Ha is different than what you should be testing.  This conference will close for participation on 2 March at 23:59 pm, Eastern Standard Time (USA state of Maryland time zone), so don't delay; make your posting today!

When responding to this activity, please type your state's name into the subject box.

Part I - Hypothesis Testing Activity about mu (Chapter 8 material)

According to a report of all homes in the USA, the average size is 2100 square feet.  Compare the sample mean of the sizes shown in Part 3, Cell H44, of your spreadsheet to 2100, and then reasonably make one of the following claims:  In 'Your State's Name goes here' the average size of all homes for sale by owner is less than 2100 square feet; In 'Your State's Name goes here' the average size of all homes for sale by owner is not appreciably different than 2100 square feet; In 'Your State's Name goes here' the average size of all homes for sale by owner is greater than 2100 square feet.  Using alpha = 0.01, test the claim you made by answering parts a-e below.

Note:  You can either invoke the Centeral Limit Theorem, or you must assume that the size data can be considered as coming from a population that is approximately normally distributed in order to use the t-distribution to find the critical value(s).  Also, you should use the size statistics located in Part 3 of your spreadsheet when computing the test statistic value for part c.

1. State the null and alternative hypotheses, Ho and H1.
1. State the critical value or values.
1. State the test statistic value.
1. Based upon your previous answers to parts a-c, is your decision to reject Ho or to fail to reject Ho?
1. Summarize your results by stating the conclusion regarding the claim.

Part II - Hypothesis Testing Activity about two variances (Chapter 9 material)

When answering parts f-j below, assume that the population distribution of trimmed prices for your state, as well as for Idaho, is normally distributed.  Make this assumption for your state even if the distribution of the trimmed prices is still slightly skewed and/or still contains any outliers (hopefully just mild, not extreme). Consider all the homes listed for sale in 'your state's name goes here' and all the homes listed for sale in Idaho.  Can the population variances of the advertised selling prices of all (reasonably priced) homes in these two states be assumed to be equal?  Use a 0.02 significance level to test this claim by filling in the blanks below.

f.     The null hypothesis is Ho:___________.

g.     The alternative hypothesis is H1:____________.

h.     The claim will be located in ______ (Ho, H1­).  Fill in this blank with the appropriate selection from within the parenthesis that follows it.

i.     Using the p-value method of hypothesis testing (see Part 13 of your spreadsheet for the p-value for this hypotheses test), the appropriate decision is to _____________ (reject, not reject) Ho.  Fill in the blank above with the appropriate selection from the parenthesis that follows it.

j.     The reason that justifies the decision made above is ___________________________________.

 Subject Mathematics Due By (Pacific Time) 02/18/2014 06:00 pm
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