H0: p=0.9Ha: p≠0.91) We know that the sample size is 1,429. For what sample proportion would the p-value be equal to 0.01. Assume that all conditions necessary for inference are satisfied.2) 400 students were randomly sampled from a large university, and 239 said they did not get enough sleep. Conduct a hypothesis test to check whether this represents a statistically significant difference from 50%, and use a significance level of 0.01.3) Given the same situation above (n = 400, p-hat = 239/400) set up a confidence interval at the 95% confidence level.4) Use the confidence interval you found in part (3) above to conduct a hypothesis test on ‘Do less than half of college students get enough slee

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.