Final answer:
The two-tailed p-value for a one-sample t-test with a t-statistic of -1.52 and 7 subjects (6 degrees of freedom) is 0.0095. The p-value is significant if the alpha level is greater than 0.0095. Calculations involve using the Student's t-distribution and interpreting results relative to the alpha level.
Step-by-step explanation:
The student is asking about how to find the two-tailed p-value when conducting a one-sample t-test based on a sample size of 7. Given that the t-statistic is -1.52, we use the Student's t-distribution with 6 degrees of freedom (df = n - 1) to find the p-value. Since the t-distribution is symmetrical, the p-value for a two-tailed test is twice the one-tailed p-value. The provided p-value using the Student's t-distribution is 0.0095, indicating a significant result if the alpha level set for the test is higher than 0.0095.
For other similar calculations, instructions were provided on how to perform such tests using a graphing calculator, entering the necessary values for the null hypothesis, alternative hypothesis, sample mean, sample standard deviation, and sample size to obtain the test statistic and the p-value. The alternative hypothesis is defined based on whether we are testing for a mean greater than, less than, or different from the hypothesized population mean.
In the example where a student conducts an independent-samples t-test with sample size 10 in each of two groups with alpha = 0.01, the p-values that would lead to a rejection of the null hypothesis would be any p-values less than 0.01 for a two-tailed test. Similarly, one can determine the necessary p-value to either reject or fail to reject the null hypothesis for other scenarios using the calculator's functions and interpreting the results against the chosen significance level.