Elementary Statistics: Could Use Some Help PART 2

Discussion in 'Community Discussion' started by HappyDude20, Dec 8, 2010.

  1. HappyDude20 macrumors 68020

    HappyDude20

    Joined:
    Jul 13, 2008
    Location:
    Los Angeles, Ca
    #1
    Hi guys, about 2 months ago I created a thread asking for help and truth be told, received more help from this forum than I perhaps deserved.

    I have about 7 math exercises to complete and just like the last thread 2 months ago, I'd appreciate any guidance towards understanding how to solve each math problem, much more than simply receiving the answers..though those don't hurt either. :D

    Elementary Statistics - Ch. 8 & Ch. 9

    Specifically:

    Ch. 8.3 - Testing a Claim About a Proportion
    Ch. 8.5 - Testing a Claim About a Mean: Not Known
    Ch. 8.6 - Testing a Claim About a Standard Deviation or Variance

    &

    Ch. 9.2 - Inferences About Two Proportions

    -------------------------

    Exercises


    1. Government officials claim that 29% of the residents of a state are opposed to building a nuclear plant to generate electricity. To test the government's claim, an independent testing group selects a random sample of 81 state residents and finds that 38 of the people are opposed to the nuclear plant. Can we conclude that the government's claim is inaccurate? Use a 0.05 level of significance.

    2. In one study of 71 zombies enrolled in a "try to quit eating brains" treatment (based on data from "Juicy Brain Therapy" by Eddie, Journal of the Ghoul MEdical Association) it was found that 39 of them quit eating brains after one year. Use a 0.05 significance level to test the claim that among 71 zombies who tried to quit with "Juicy Brain Therapy", the majority are still eating brains a year after treatment.

    3. A new weight-reducing pill is being sold. The manufacturer claims that an overweight person who takes this pill as directed will lose an average of 15 pounds within a month. To test this claim, a doctor gives this pill to six overweight perople and finds that they lose an average of only 12 pounds with a standard deviation of 4 pounds. Can we reject the manufacturers claim?

    4. The sugar content in different boxes of the Count Chocula Cereal was pointed out by a mindful consumer. The amounts were summarized in the following statistics: n=16, x-bar (you know, x with the line over it)=0.295g, s=0.168.
    Use a 0.005 significance level to test the claim that the mean sugar content of the Count Chocula Cereal is less than 0.3g.

    5. Tests in Eddie's past statistics classes have scores with a standard deviation equal to 14.1
    One of this recent classes has 27 test test scores with a standard deviation of 9.3. Use a 0.01 significance level to test the claim that this current class has less variation than past classes.

    6. Are men and women college students equally likely to be frequent binge drinkers?
    Men: n=7180, x=1630
    Women: n=9916, x=1684

    6a. Test the claim that men and women college students binge drink at an equal rate. Use a 0.10 significance level.

    6b. Construct a 90% confidence interval for the difference between the binge drinking rates of college men and college women.


    7. In a study of color blindless, 400 priests and 2000 nuns are randomly slected and tested. Among the priests, 40 have color blindness. Among the nuns, 120 have color blindness.

    7a. Test the claim that priests have a higher rate of color blindness than nuns. Use a 0.05 significance level.

    7b. Construct a 95% confidence interval for the difference between the color blindness rates of priests and nuns.

    -------

    So far, I believe most, if not all, deals with null hypothesis; you know, testing with Ho & h1. Of which i'm somewhat confused over...but nevertheless.

    I'll be in front of my MBP studying for most of the day, ready to respond to any help. I'll also for a bit be going to my college's math lab asking for help.
     
  2. swiftaw macrumors 603

    swiftaw

    Joined:
    Jan 31, 2005
    Location:
    Omaha, NE, USA
    #2
    Stats professor here, so I'll give it my best shot :)

    Looks like you are studying hypothesis tests. The idea is you have two hypotheses, the null hypothesis H0 and the alternative hypothesis H1. The idea is that we assume H0 is true unless there is enough evidence in the data to convince us that H1 is true instead.

    (Think of the criminal trial analogy where H0 is that the defendant is innocent and H1 is that the defendant is guilty).

    What is this 'evidence'? The evidence we are looking for is witnessing something that would be very unlikely to occur under our assumption that H0 is true. Thus we would conclude that either H0 is true and we witnessed a freak event, or H1 is true instead. By occum's razor we therefore conclude that H0 is false and H1 is true.

    How much 'evidence' we need is governed by the significance level of the test. For example, a significance level of 0.05 for example means that we want a 5% probability of rejecting H0 when it is in fact true.

    The specifics of each test (means, variances, proportions) is based on the sampling distribution of the relevant test-statistic, which can be found in the appropriate text sections.
     

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