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3. Responses to a survey question are broken downaccording to employment status andthe sample results are given below. At the 0.10significance level, test the claim...

Question

3. Responses to a survey question are broken downaccording to employment status andthe sample results are given below. At the 0.10significance level, test the claim thatresponses and employment status areindependent.YESNOUNDECIDEDTOTALEMPLOYED40258UNEMPLOYED25155TOTALUse these formulas given below. Test statisticx^2=∑(O-E)^2/E where O is the observed frequency in a cell and E isthe expected frequency found by evaluating: OR USE TECHNOLOGYE=(row total)(column total)/(grand total) ,df=(r-1)(c-1)

3. Responses to a survey question are broken down according to employment status and the sample results are given below. At the 0.10 significance level, test the claim that responses and employment status are independent. YES NO UNDECIDED TOTAL EMPLOYED 40 25 8 UNEMPLOYED 25 15 5 TOTAL Use these formulas given below. Test statistic x^2=∑(O-E)^2/E where O is the observed frequency in a cell and E is the expected frequency found by evaluating: OR USE TECHNOLOGY E=(row total)(column total)/(grand total) , df=(r-1)(c-1) 2ND[x^-1]--> EDIT -->1:[A] 2x3→ Enter the values in the MATRIX Then: STAT → TESTS → x^2 -- Test → Calculate and press ENTER



Answers

Use the following information. The frequencies in a contingency table can be written as relative frequencies by dividing each frequency by the sample size. The contingency table below shows the number of U.S. adults (in millions) ages 25 and over by employment status and educational attainment. (FIGURE CAN'T COPY) What percent of U.S. adults ages 25 and over (a) have a degree and are unemployed? (b) have some college education, but no degree, and are not in the labor force? (c) are employed and high school graduates? (d) are not in the labor force? (e) are high school graduates?

We have that contingency table that we have with relative frequencies from the previous exercises and we cannot use the chi squared with those values you must have the actual counts. They cannot be relative frequencies. They must be whole numbers. They must behold numbers. Yeah. If you try to use the software and you put in the counts as relative frequencies you will get a domain air so you must put them in as counts because the chi squared statistic wants to know the actual number and then the expected values can be decimals but the outcomes that you have must be whole numbers. Okay.

So in this question, we want to find basically a conditional probability, and we want to find what's the probability given that someone has a degree? So we're only going to use that last column. What's the likelihood of finding someone who is not in the labor force? And so just using this column, we can find that not in the labor force is this cell right here, so that is 23.43%. That's that conditional probability.

So we want to use our relative frequency conditional uh, distribution or table by columns for this question. And we really want to find what's the probability that, given someone has not graduated from high school, So they have less than a high school graduation degree? What's the probability that they are unemployed or not employed? And we're only going to use this column? And this is our answer. So 7.36%. If this were a regular relative frequency, we would have to do a division to find that answer. But for this one, because of the distribution being set up to be a conditional probability based on columns, all we have to do is write down that cell team.

So in this problem, we want to again use our contingency table that has the relative frequencies, and we want to find for those people who are not in the labor force. So the condition is not in the labor force, we're going to use that last row. We want to know what's the likelihood that the person has some college? And This is the cell we want .1614, Which is 16.14%. Yeah.


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