A cookie company intends to include an average of 9 or more chocolate chips in every cookie. If the production line is putting in an average of less than 9 chips per cookie the company will shut down the line for repairs. They take a random sample of 4 cookies and find that the average number of chocolate chips per cookie in the sample was 7 with a sample standard deviation of 2. Assume that the number of chocolate chips in a cookie has approximately a symmetric distribution. Using LaTeX: \alpha=0.05\:α = 0.05, conduct a hypothesis test and state your conclusion. Be sure to follow all ten steps for a complete hypothesis test.

The resumâ´es of two male applicants for a college teaching position in chemistry are placed in the same file as the resumâ´es of two female applicants. two positions become available, and the first, at the rank of assistant professor, is filled by selecting one of the four applicants at random. the second position, at the rank of instructor, is then filled by selecting at random one of the remaining three applicants. using the notation m2f1, for example, to denote the simple event that the first position is filled by the second male applicant and the second position is then filled by the first female applicant, (a) list the elements of a sample space s; (b) list the elements of s corresponding to event a that the position of assistant professor is filled by a male applicant; (c) list the elements of s corresponding to event b that exactly one of the two positions is filled by a male applicant; (d) list the elements of s corresponding to event c that neither position is filled by a male applicant; (e) list the elements of s corresponding to the event a â© b; (f) list the elements of s corresponding to the event a âş c; (g) construct a venn diagram to illustrate the intersections and unions of the events a, b, and c.