Adata set includes data from student evaluations of courses. the summary statistics are n=87, x =4.16, s=0.59 use a 0.05 significance level to test the claim that the population of student course evaluations has a mean equal to 4.25 assume that a simple random sample has been selected. identify the null and alternativehypotheses, test statistic, p-value, and state the final conclusion that addresses the original claim.

Atextile fiber manufacturer is investigating a new drapery yarn, which the company claims has a mean thread elongation of 12 kilograms with a standard deviation of 0.5 kilograms. the company wishes to test the hypothesis upper h subscript 0 baseline colon mu equals 12 against upper h subscript 1 baseline colon mu less-than 12 using a random sample of n equals 4 specimens. calculate the p-value if the observed statistic is x overbar equals 11.8. round your final answer to five decimal places (e. g. 98.76543).