Spider-Man is trying out a new web-making formula and wants to know if it will yield more stable results. His supervisor, Happy, claims that the old process creates webs with normally distributed tensile strengths with = 0.3 GPA. Spiderman collects 15 measurements from webs using the new formula and finds a sample standard deviation of s = 0.23 GPA.

(a) (1 point) Perform a hypothesis test at = 0.05 by hand to test whether there is sufficient evidence to suggest that the new formula is better (has less variability) than the original.

(b) (0.5 points) Suppose that Spiderman now takes 100 measurements (instead of 15) and still finds a sample standard deviation of 0.23 GPA. Perform a hypothesis test at = 0.05 by hand to test whether there is sufficient evidence to suggest that the new suit is better (more accurate) than the original.