Final answer:
The question involves conducting hypothesis tests to assess the mean I.Q. of brown trout against a value of 4. Using a Student's t-test at a 0.05 significance level, we can test different hypotheses. An example conclusion may indicate insufficient evidence to reject the null hypothesis based on the given sample IQ scores, p-value, and confidence interval.
Step-by-step explanation:
The question asks to conduct a hypothesis test to determine the mean I.Q. of brown trout in a variety of scenarios, comparing it to a value of 4. The hypothetical context provided mentions a belief that the average brown trout's I.Q. is greater than four, and IQ readings have been recorded for a sample of 12 brown trout. This information can be used to perform different types of hypothesis tests, including one-tailed and two-tailed tests. Depending on the hypothesis, we would conduct a test to see if the mean is equal to, not equal to, less than, or greater than four.
Hypothesis Testing Steps
- Formulate the null and alternative hypotheses for each scenario. For example, the null hypothesis (H0) may state that the mean I.Q. is equal to 4, while the alternative hypothesis (Ha) may suggest it is not equal to, less than, or greater than 4 depending on the test.
- Determine the appropriate statistical test. In this case, based on the provided information, a Student's t-test would be suitable as the sample size is small and standard deviations are unknown.
- Calculate the test statistic, which is a t-score in this context.
- Compare the calculated t-score to the critical t-value at the chosen significance level (Alpha: 0.05), and determine the p-value.
- Draw a conclusion based on the comparison of the p-value and the significance level.