A well-known brokerage firm executive claimed that at least 90% of investors are currently confident of meeting their investment goals. An XYZ Investor Optimism Survey, conducted over a two week period, found that in a sample of 800 people, 88% of them said they are confident of meeting their goals.

a) For this claim state the null and alternative hypothesis as an expression: (multiple choice)

A. H0:?=0.9

HA:??0.9

B. H0:p=0.9

HA:p<0.9

C. H0:?=0.9

HA:?>0.9

D. H0:?=0.9

HA:?<0.9

E. H0:p=0.9

HA:p>0.9

F. H0:p=0.9

HA:p?0.9

b) State the null hypothesis as a complete sentence:

State the alternative hypothesis as a complete sentence:

This test would require a test. (multiple choice)

a. right-tailed

b. quad-tailed

c. left-tailed

d. two-tailed

c) How could we re-write the claim to make this a two-tail test? (sentence)

d) Test the claim that the proportion of people who are confident is smaller than 90% at the 0.05 significance level. Determine the following:

The test statistic: (round to the 3rd decimal)

The p-value: (round to the 4th decimal)

e) What would be our formal conclusion about the null hypothesis at a 0.05 significance level?

Erin bought christmas cards for $2 each to send to her family and friends. which variable is the dependent variable?

After a dreary day of rain, the sun peeks through the clouds and a rainbow forms. you notice the rainbow is the shape of a parabola. the equation for this parabola is y = -x2 + 36. graph of a parabola opening down at the vertex 0 comma 36 crossing the x–axis at negative 6 comma 0 and 6 comma 0. in the distance, an airplane is taking off. as it ascends during take-off, it makes a slanted line that cuts through the rainbow at two points. create a table of at least four values for the function that includes two points of intersection between the airplane and the rainbow. analyze the two functions. answer the following reflection questions in complete sentences. what is the domain and range of the rainbow? explain what the domain and range represent. do all of the values make sense in this situation? why or why not? what are the x- and y-intercepts of the rainbow? explain what each intercept represents. is the linear function you created with your table positive or negative? explain. what are the solutions or solution to the system of equations created? explain what it or they represent. create your own piecewise function with at least two functions. explain, using complete sentences, the steps for graphing the function. graph the function by hand or using a graphing software of your choice (remember to submit the graph).

Which elements in the set are integers? –8, 3⁄4, √ 18 , 0, √ 16 , 5, –2⁄7, 6 a. –8, 0, 5, 6 b. –8, 0, √ 16 , 5, 6 c. 3⁄4, √ 18 , √ 16 , 5, –2⁄7 d. –8, 0, √ 18 , 5, 6