Analyzing Conditional Probabilities in Data Science Employment

30 Pts Read and c 1 1a 1 1b 1 1c 1 1d 1 2 1 3 1 4 2 5 2 6 3 7 1 1 1a 1 1b 1 1c A. The U.S. right repres Census Bur B . The ques experience

1 1d 1 2a 2 2b 3 2c 3 1 3a 1 3b 1 3c 1 3d 1 3e 1 3f

complete the questions below: What is the first random experiments? What are the outcomes of the first random experiment? What is the second random experiments? What are the outcomes of the second random experiment? What is the probability that the head of one of these households has a Bachlor’s degr P(B)= What is the probability that the household income is under $25,000? P(W)= P(B∩W)= P(W|B)= P(B|W)= Answer below: Explain and distinguish the meanings of the above two conditional pr P(W|B): Probability that a household earns $25,000 or less given that the hea This conditional probability assesses the likelihood of a specific income level ($25,0 P(B|W): Probability that the head of a household has a Bachelor's degree given This conditional probability evaluates the likelihood that the head of a household hol P(W|B) considers the probability of income level given a specific educational attainm P(B|W) considers the probability of educational attainment given a specific income l Event A: List two outcomes of Event A: Event B: . Census Bureau is a leading source of quantitative data related to the people and eco sents the number of households (thousands) and the household income by the highest reau web site). Use this crosstabulation to answer the following questions. What is the joint probability that the head of one of these households has a Bachelor' $25,000? What is the probability that a household earns $25,000 or less out of all the househol What is the probability that the households headed by someone with a Bachelor's de distinguish stions below are to analyze a dataset for job positions in Data Science in 2023. It inc level, and salary. It also details the company location, the residence of the employee, What are the two random experiments (events) from the summary Table 1 ? Answer

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List two utcomes of Event B: P(Entry)= P(Entry| Small)= To determine if experience level and company size are independent, we can com From the calculations: P(Entry) = 24.10% P(Entry|Small) = 41.01% Since P(Entry|Small) ≠ P(Entry), we can conclude that experience level and company What we learn about the chances of finding an entry level data job from the res The chances of finding an entry level data job vary depending on the size of the co Entry level data jobs are more likely to be found in small companies compared to This insight helps in understanding the relationship between experience level and What is the probability that a job position is for the entry level? Use cell reference fro What is the conditional probability of finding an Entry Level job from those in Sma From the above two questions, are Experience Level and the Company size of a job p the chances of finding an entry level data job from the results of this independent test Compute the expected values for the average salary associated with experience level and company size. Calculate with cell references from the summary Table 2 . Entry-level Expected Average Salary = Mid-level Expected Average Salary = Entry-level Expected Variance for Average Salary = Mid-level Expected Variance for Average Salary = Entry-level Expected standard deviation for Average Salary = Mid-level Expected standard deviation for Average Salary =

The first random experiment is selecting a household fro The outcomes of the first random experiment are the diff The second random experiment is determining the house The outcomes of the second random experiment are the d ree? 0.3371 0.2000 0.0378 0.1122 0.1892 robabilities (P(W|B) and P(B|W). ad of the household has a Bachelor's degree. 000 or less) among households where the head of the hous that the household earns $25,000 or less. lds a Bachelor's degree when we already know the househ ment. level. Experience Level Entry Level, Mid Level Company Size onomy of the United States. The crosstabulation on the t level of education for the head of household (U.S. 's degree while the household is earing less than lds headed by someone with a Bachelor's degree ? egree out of all the households earn $25,000 or less? cludes information as job title, employment type, , and the size of the compan. below:

Large, Medium, Small 24.10% 0.41% mpare the conditional probability of finding an Entry L If P(Entry|Small) ≈ P(Entry), then they are independent. If P(Entry|Small) ≠ P(Entry), then they are dependent. y size are dependent. sults of this independent test: ompany. medium or large companies. company size, providing valuable information for job see $98,736.34 $135,602.04 $23,893,787.26 $14,655,785.97 $4,888.33 $3,830.02 om Table 1 . all sized companies? Use cell reference from Table 1 . position independent? Why? What can we learn about t?

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om the given data. ferent categories of highest level of education: High school graduate (H), Bachelor's degree (B), Master's degree (M), ehold income level based on the selected household. different income categories: Under $25,000 (W), $25,000 to $49,999 (X), $50,000 to $99,999 (Y), and $100,000 and sehold holds a Bachelor's degree. It's calculated by dividing the number of households with both a Bachelor's degree a hold income is $25,000 or less. It's calculated by dividing the number of households with both income under $25,000

Level job regardless of company size with the overall probability of finding an Entry Level job. ekers or employers targeting specific demographics.

Household Income Highest Level of Education Total H: High school graduate 9880 9970 9441 3482 32773 B: Bachelor’s degree 2484 4164 7666 7817 22131 M: Master’s degree 685 1205 3019 4094 9003 D: Doctoral degree 79 160 422 1076 1737 Total 13128 15499 20548 16469 65644 er of households with Bachelor's degrees. of households with income under $25,000. Table 1 Percent of Jobs by Company Size Large Medium Small Total Experience level: Entry 3.15% 18.92% 2.03% 24.10% Experience level: Mid 3.15% 69.82% 2.93% 75.90% W: Under $25,000 X: $25,000 to $49,999 Y: $50,000 to $99,999 Z: $100,000 and more

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Total 6.31% 88.74% 4.95% 100.00% Table 2 Percent of Jobs by Company Size Average S Large Medium Small Total Large Experience level: Entry 13.08% 78.50% 8.41% 100.00% $ 104,622.86 Experience level: Mid 4.15% 91.99% 3.86% 100.00% $ 132,228.57 Grand Total 6.31% 88.74% 4.95% 100.00% $ 118,425.71 Salary Dev Large Experience level: Entry -$13,802.85 Experience level: Mid $13,802.86 Optional:Table for Salary Deviations

Salary by Company Size Medium Small $ 100,927.65 $ 69,244.44 $ 13,684.67 $ 79,228.21 $ 5,823.46 $ 137,524.11 $ 93,422.92 $ 5,487.49 $ 126,508.43 $ 3,606.12 $ 129,721.82 $ 83,531.73 viation by Company Size Medium Small -$17,498.06 -$49,181.27 $7,802.29 $8,891.19

$ 98,736.34 $ 135,602.04

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$ 104,622.86 $ 100,927.65 $ 69,244.44 104622.857143 100927.7

69244.44 378185403.62

575_E4_Salgueiro

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