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Example When flipped 1000 times, a coin landed 515 times heads up. Does it support the hypothesis that the coin is unbiased ?

Solution: The null hypothesis is that the coin is unbiased.

In notations Ho : P = Po where Po = 0.5 and qo = 1 - Po = 0.5

Now the sample proportion is P' = = 0.515

We then reject the null hypothesis. The coin is not unbiased.

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Example While throwing 5 die 40 times, a person got success 25 times - getting a 4 was called success. Can we consider the difference between expected value and observed value as being significantly different ?

Solution: If we carefully examine the data then the hypothesis can be stated that the dice is unbiased.

In notation Ho : P = Po where

i.e. Ho : P = 0.4019 and Ha : P ¹ 0.4019

The sample proportion P' = = 0.625

Hence the hypothesis Ho is to be rejected at 1% level of significance or we can say that the value obtained is highly significant. The given data do not support Ho. Thus the dice is not unbiased.

Example A patented medicine claimed that it is effective in curing 90% of the patients suffering from malaria. From a sample of 200 patients using this medicine, it was found that only 170 were cured. Determine whether the claim is right or wrong. (Take 1% level of significance).

Solution: The null hypothesis is that the claim is quite right.

i.e. Ho : P = Po where Po = 90% = 0.9 and Ha : P ¹ 0.9.

Also qo = 0.1 and n = 200.

The sample proportion P' = = 0.85

The null hypothesis Ho is quite right at 1% level of significance and that the claim is justified.

Index

8.1 Population
8.2 Sample
8.3 Parameters and Statistic
8.4 Sampling Distribution
8.5 Sampling Error
8.6 Central Limit Theorem
8.7 Critical Region
8.8 Testing of Hypothesis
8.9 Errors in Tesitng of Hypothesis
8.10 Power o a Hypothesis Test
8.11 Sampling of Variables
8.12 Sampling of Attributes
8.13 Estimation
8.14 Testing the Difference Between Means
8.15 Test for Difference Between Proportions
8.16 Two Tailed and one Tailed Tests
8.17 Test of Significance for Small Samples
8.18 Students t-distribution
8.19 Distribution of 't' for Comparison of Two Samples Means Independent Samples
8.20 Testing Difference Between Mens of Two Samples Dependent Samples or Matched Paired Observations
8.21 Chi-Square
8.22 Sampling Theory of Correlation
8.23 Sampling Theory of Regression

Chapter 1