Final answer:
The p-value and critical value are part of hypothesis testing in statistics, determined using the sample mean, standard deviation, and size. Specific values cannot be calculated without additional information, such as a hypothesized population mean or a significance level. To find these values exactly, one would typically use a t-distribution and reference a t-table or use statistical software.
Step-by-step explanation:
The question is about finding the p-value and critical value for a given sample with its mean and standard deviation, assuming the population is normally distributed. Using the provided sample mean of 58.5, a standard deviation of 7.5, and a sample size of 29, one would typically use a t-distribution to find the appropriate p-value and critical value because the population standard deviation is not known. However, to calculate these without a specific test statistic or hypothesis is not possible. Normally, the p-value is found by comparing the sample mean to a hypothesized population mean and then using a t-table or statistical software to find the probability of observing such a mean or more extreme under the null hypothesis.
To find the critical value for a specified significance level (usually denoted by alpha, α), one would reference a t-table using n - 1 degrees of freedom (df = 29 - 1 = 28 in this case) and the desired level of confidence. The p-value could then be compared to the significance level to determine whether the results are statistically significant.