1.Recent studies have investigated the relationship between gender and career advancement. The following data represent a random sample of mathematicians classified by gender and academic rank. Using the following data, test for a relationship between gender and academic rank. a. State the null and alternative hypotheses (2 pts). b. Calculate the test statistic and determine the critical value (10 pts) c. Determine whether your results are significant – indicate how you know (2 pts) d. State your conclusions in one or two sentences. (2 pts) Academic Rank InstructorAssistant ProfessorAssociate ProfessorFull ProfessorTotal Female121518752 Male2125302298 Total33404829150 g

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for

the answer is c: divide the arc's degree measure by 360°, then multiply by the circumference of the circle.

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