A hypothesis is a statement or claim about a population, often making assumptions regarding a population parameter. For instance:
i. The weight of an adult Bunaji bull is 300 kg.
ii. The weight of local chicken eggs in Nigeria is 30 g.
iii. The average flock size of a rural poultry farmer is 10 chickens.
Each of these statements could either be true or false. The purpose of hypothesis testing is to assist in determining which alternative hypothesis should be accepted.
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Types of Statistical Inference
There are two common types of statistical inference:
1. Confidence intervals: Used when the goal is to estimate a population parameter.
2. Test of significance: Applied when the aim is to assess the evidence provided by a dataset concerning a claim about the population being studied.
Formulating Null and Alternative Hypotheses
The first step is to decide on the statement to be tested. For example:
i. Null Hypothesis (H0): There is no difference between the weight of a Bunaji bull and a Bunaji cow at one year of age.
ii. Alternative Hypothesis (H1 or HA): The weight of a Bunaji bull and cow differs at one year of age.
The alternative hypothesis always asserts that something is different from a specific value or expectation. The null hypothesis is denoted as H0, while the alternative hypothesis is written as H1 or HA. For example:
- H0: µ1 = µ2
- H1: µ1 ≠ µ2
Hypotheses can also be formulated based on prior knowledge. For instance, if it is known that the average body weight of a ram is 35 kg, the null hypothesis may state that the average weight of a West African Dwarf Ram is 35 kg. The alternative hypothesis would suggest that the average weight differs from 35 kg:
- H0: µ = 35 kg
- H1: µ ≠ 35 kg
In hypothesis testing, H0 will only be rejected in favor of H1 if the evidence strongly suggests that H0 is false. Otherwise, H0 will not be rejected, leading to two possible conclusions: reject H0 or fail to reject H0.
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Test Statistics for Hypothesis Testing
The goal of a statistical test is to determine whether a given dataset is sufficiently different from what would be expected under the null hypothesis. After formulating a hypothesis, a test procedure is applied based on a sample drawn from the population of interest.
The test statistic chosen serves as the decision maker for rejecting or not rejecting H0. Generally, if the test statistic computed from the sample is very different from what would be expected under H0, the null hypothesis should be rejected. However, if the statistic is consistent with H0, there is no strong reason to reject it.
Example: Thirty ShikaBrown layer chickens were randomly selected from a population at the National Animal Production Research Institute, Shika Zaria. The average reported body weight for ShikaBrown layers is 2500 g with a standard deviation of 250 g at 40 weeks of age. The sample data is as follows:
S/N40 wks (gm)S/N40 wks (gm)123001625002240017250032100182200…………302000
The average body weight of the sample is 2260 g.
i. Null Hypothesis (H0): µ = 2500 g.
ii. Alternative Hypothesis (Ha): µ ≠ 2500 g.
The sample mean of 2260 g is different from the population mean of 2500 g, but is the difference significant enough to reject the null hypothesis? The answer depends on the variability of body weight at 40 weeks.
The standard deviation of the sample mean (σx) is 45.64. Using a t-statistic, the calculated value for z is -5.25. The critical z-score for α = 0.05 in a two-tailed test is ±1.96. Since the calculated z-score falls outside the range of -1.96 to 1.96, the null hypothesis is rejected.
One-Tail vs. Two-Tail Tests
A two-tailed test allots half of the significance level (α) to each tail, testing the possibility of deviation in both directions. A one-tailed test, on the other hand, allocates all of α to one tail, testing deviation in only one direction. One-tailed tests are more powerful in detecting effects in one direction but ignore the possibility of deviation in the other.
Error Types in Hypothesis Testing
1. Type I Error: Occurs when the null hypothesis is true, but is incorrectly rejected. The probability of making a Type I error is denoted as α.
2. Type II Error: Occurs when the null hypothesis is false, but is incorrectly accepted. The probability of making a Type II error is denoted as β. The risk of
Type II errors can be reduced by ensuring the test has enough power, often by increasing the sample size.
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Frequently Asked Questions
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