Answer:
Explanation:
Here's a step-by-step explanation of how to calculate the p-value for the hypothesis test:
Step 1: State the null and alternative hypotheses
The null hypothesis is that the true population mean weight of stoaches is 308 g, and the alternative hypothesis is that the true population mean weight is not 308 g.
H0: µ = 308 g (null hypothesis)
Ha: µ ≠ 308 g (alternative hypothesis)
Step 2: Determine the test statistic
We can use a t-test to determine the test statistic for this hypothesis test. The test statistic is given by:
t = (sample mean - hypothesized mean) / (standard error of the mean)
where the sample mean is 313.8 g, the hypothesized mean is 308 g, and the standard error of the mean is calculated as:
standard error of the mean = standard deviation / sqrt(sample size)
Substituting the given values, we get:
t = (313.8 - 308) / (58 / sqrt(54))
t = 1.547
Step 3: Determine the p-value
To determine the p-value, we need to find the probability of obtaining a test statistic as extreme or more extreme than our observed t-value, assuming the null hypothesis is true. Since we have a two-sided alternative hypothesis, we need to find the area in both tails of the t-distribution that is more extreme than our observed t-value.
Using a t-distribution table or calculator with 53 degrees of freedom (since we have a sample size of 54), we find that the probability of obtaining a t-value of 1.547 or greater is 0.0722 in the right tail, and the probability of obtaining a t-value of -1.547 or less is also 0.0722 in the left tail. Therefore, the p-value for the two-sided test is the sum of these two probabilities:
p-value = 0.0722 + 0.0722
p-value = 0.1444
Step 4: Compare the p-value to the significance level
The significance level is typically set to 0.05 for hypothesis tests. Since our calculated p-value (0.1444) is greater than the significance level of 0.05, we fail to reject the null hypothesis. This means that we do not have sufficient evidence to suggest that the true population mean weight of stoaches is different from 308 g.
In summary, the p-value for the two-sided hypothesis test is 0.1444, and since this value is greater than the significance level of 0.05, we do not reject the null hypothesis.