Null Hypothesis, Deviation

Date: 08/09/97 at 18:57:35
From: Heather
Subject: Statistics

A statistician believes that on the average the members of a group of 
people weigh 120 pounds. To test this belief, the statistician
weighs 7 people with the following results:

  121, 125, 118, 130, 117, 123, 120

  a. What is the statistician's null hypothesis?
  b. What is the alternative hypothesis?
  c. What mean and standard deviation would you estimate from the  
     given data?
  d. What conclusion would you draw about the statistician's belief 
     at the 5 percent significance level?

Thanks.

Date: 08/09/97 at 19:54:27
From: Doctor Anthony
Subject: Re: Statistics

>a. What is the statistician's null hypothesis?

    That the average is 120 pounds.

>b. What is the alternative hypothesis?

    That the average differs from 120 - either higher or lower.

>c. What mean and standard deviation would you estimate from the 
    given data?

    Mean of sample is  854/7 =  122

    sample variance = 104308/7 - 122^2  = 17.143    s.d = 4.1404

    Best estimate of population variance = (7/6)(17.143) = 20.00

      "         "          "        s.d  =   4.472

    The s.d. of the sampling distribution is  4.472/sqrt(7) =  1.690
    (also known as standard error of the mean)

>d. What conclusion would you draw about the statistician's belief at 
    the 5 percent significance level?

                            122 - 120
    We compute z from   z = ---------  =  1.1832
                              1.69

    We compare this value against a z value of 1.96, which is the 
    two-tailed significance threshold for the 5-percent level 
    (2.5 percent in each tail).

    Since  1.18 < 1.96 our result is not significant, and we do not  
    reject the null hypothesis that the mean is 120 pounds. This does 
    not mean that it is 120, but a sample, size 7, from a population 
    with mean 120 has a better than 5 percent probability of giving a 
    mean as high as 122.

-Doctor Anthony,  The Math Forum
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