Solved assignment aiou 3447 statistics for mangement

           ALLAMA IQBAL OPEN UNIVERSITY ISLAMABAD (AIOU)


STATISTICS FOR MANAGEMENT (3447)                                                     AUTUMN 2016

                                                  ASSIGNMENT NO 2

PART 1: Q1 (a,b)

Q1:Explain in detail the procedure of testing a null hypothesis with suitable example?

A:MAKING A FORMAL STATEMENT FOR NULL HYPOTHESIS:

In hypothesis testing,we must state the assumed or hypothesized value of the population parameters before we began sampling.The assumption we wish to test is called
the NULL HYPOTHESIS and is symbolized "Ho" or "H sub-zero".
Suppose we want to test the hypothesis that the population mean is equal to 500.We would symbolize it as follows and read it."The null hyothesis is that the population mean is equal to 500".
                                  Ho = µ = 500
The term null hypotesis arises from earlier agricultural and medical applications of statistics .
In order to test the effectiveness of a new fertilizer or drug: The tested hypothesis (the null hypothesis ) was that it had no effect , that is there was difference
treated and untreated samples.
If we use a hypothesized value of a population mean in a problem , we would represent it symbolically as
                                       
" µHo "
This is read as ,"The hypothesized value of population mean".

If our sample result fail to support the null hypothesis ,we must conclude that some thing else is true. Whenever we reject the hypothesis, the conclusion we do accept
is called the alternative hypothesis and is symbolized H1 ("H sub-one").For the null hypothesis

Ho = µ =200
(Read,"the null hypothesis is that the population mean is equal to 200")

We will consider 3 possible alternate hypothesis:
               H1 : µ ? 200  (the alternate hypothesis that mean is not equal to 200)
      H1 : µ > 200  (the alternate hypothesis that mean is greater than 200)
               H1 : µ < 200  (the alternate hypothesis that mean is less than 200)

The purpose of hypothesis testing is not to question the computed value of the sample statistic but not to make a judgement about the difference b/w that sample
statistic and a hypothesized population parameter.
If we assume the hypothesis is correct ,then the significance level will indicate the percentage of sample mean that is outside certain limits.

Q1(b): For a sample of 60 women taken from a population of over 5,000 enrolled in a weight-reducing program a nationwide chain of health spas, the sample mean

 diastolic blood pressure is 101 and the sample standard deviation is 42. At a significance level of 0.02 on the average, did the women enrolled in the program

 have diastolic blood pressure that exceeds the value of 75? 

ANS: GIVEN:

   n = 60    ;   d = 42

   x = 101    ;  a = 0.02

     SOLUTION:

 

Null & alternate hypothesis

Ho : µ = 75

H1 : µ > 75

Level of significance = a = 0.02

Test statistic

     t = (x - µ)/ d/vn  (v is squre root must replace)

     t = (101- 75)/ 42/v60

     t = 4.79

 CRITICAL REGION:

     t > ta(n-1)

     t > t 0.02(60-1)

     t > t 0.02(59)

     t > 2.390     (from table)

 

CONCLUSION:

     Since Ho is rejected ,therefore the womens in program have

     blood pressure significally higher than given level which is 75.

                                                 TO BE CONTINUED ON:

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