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### 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
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
High School Statistics

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