Final answer:
The null hypothesis (H0) for testing if the mean weight of a species of flounder is less than 48 grams is stated as H0: μ = 48, while the alternative hypothesis (Ha) is Ha: μ < 48.
Step-by-step explanation:
The appropriate null and alternative hypotheses for a hypothesis test concerning whether the mean weight of a species of flounder is less than 48 grams, given a sample mean weight of 49.5 grams from 400 flounders, are formally stated as follows:
Null Hypothesis (H0):
μ = 48
Alternative Hypothesis (Ha):
μ < 48
The null hypothesis (H0) is a statement that the mean weight is equal to 48 grams. This is the hypothesis that will be tested and possibly rejected in favor of the alternative hypothesis, which states that the mean weight of the flounder is less than 48 grams. In a hypothesis test, we use sample data to determine whether there is enough statistical evidence to reject the null hypothesis.
To analyze the test, scientists would typically calculate a test statistic based on the sample mean, the hypothesized population mean, and the sample standard deviation. This test statistic is then used to find a p-value, which is compared against a chosen significance level. If the p-value is less than the significance level, the null hypothesis is rejected in favor of the alternative. Conversely, if the p-value is greater than the significance level, there is not enough evidence to reject the null hypothesis.
In the case of the student's question, scientists would perform a one-tail test (specifically a left-tailed test), as they are interested in whether the mean weight is less than a certain value.