Answer :
To test the statement that the average weight of bull-calves is more than 133.4 kg, you can use a one-sample z-test for the population mean, assuming that the weights follow a normal distribution.
We'll perform the test at three different levels of significance: α = 0.02, α = 0.05, and α = 0.10.
Here are the steps for conducting the test:
1. State the null and alternative hypotheses:
- Null Hypothesis (H0): The average weight of bull-calves (μ) is not more than 133.4 kg.
- Alternative Hypothesis (H1):
- For α = 0.02: μ > 133.4 kg (right-tailed test)
- For α = 0.05: μ > 133.4 kg (right-tailed test)
- For α = 0.10: μ > 133.4 kg (right-tailed test)
2. Calculate the sample mean and sample standard deviation:
- Sample Mean (X') is the average of the given weights.
- Sample Standard Deviation (s) is calculated from the given weights.
3. Determine the sample size (n): The total number of bull-calves in the sample.
4. Choose the level of significance (α): Given as 0.02, 0.05, and 0.10.
5. Calculate the test statistic (z):
The test statistic (z) is calculated as:
z = (X' - μ) / (s / √n)
6. Determine the critical value:
- For α = 0.02, find the critical z-value from the standard normal distribution table.
- For α = 0.05, find the critical z-value from the standard normal distribution table.
- For α = 0.10, find the critical z-value from the standard normal distribution table.
7. Compare the test statistic with the critical value:
- If the test statistic is greater than the critical value, reject the null hypothesis.
- If the test statistic is less than or equal to the critical value, fail to reject the null hypothesis.
8. Make a decision:
- For α = 0.02, 0.05, and 0.10, state whether you reject or fail to reject the null hypothesis.
9. Draw a conclusion:
- If you reject the null hypothesis, you can conclude that there is evidence to suggest that the average weight of bull-calves is more than 133.4 kg at the chosen level of significance.
- If you fail to reject the null hypothesis, you do not have enough evidence to conclude that the average weight is more than 133.4 kg at the chosen level of significance.
You will need the sample mean, sample standard deviation, and sample size to calculate the test statistic and compare it with the critical value for each level of significance. If you provide these values, I can help you with the calculations.
To know more about weights:
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