6.5 Test for Means, Variance and Proportions

3. Test for Means, Variance and Proportions

1. Testing For Means

a. Testing hypothesis for a single population mean

Consider Hypothesis testing about a population mean under three different conditions: 

When sampling is from a Normal Distributions with known variance.

When sampling is from a Normal Distributions with unknown variance.

When sampling is from a population that is not normally distributed.

For a large sample size, when sampling is from normal distribution with knownvariance, the test hypothesis is

For example:

For a random sample of 5 persons, fed on a diet A, increased weight in pounds in a certain period were: 

10, 12, 13, 11, 14 

For another random sample of 7 persons, fed on a diet B, increased weight in pounds in a certain period were: 

8, 9, 12, 14, 15, 10, 9 

Test whether the diets A and B differ significantly as regards their effect on increase in weight at 5% level of significance. 

Solution:

n1 = 5, n2 = 7 

X1 = 10, 12, 13, 11, 14 

X2 = 8, 9, 12, 14, 15, 10, 9The calculated value is less than the tabulated value and hence the null hypothesis is accepted. The experiment provides no evidence against the hypothesis. Therefore, it is concluded that diets A and B do not differ significantly as regards their effect on increase in weight is concerned.

2. Tests for Variances

a. Hypothesis Testing For a Single Population Variance

For a given data available for analysis consisting of random samples drawn from a normally distributed population, the test hypothesis used for analysis of variance is