IQ and Income Correlate Closely

IQ on “wealth, income, and financial distress” in an article for Intelligence, a peer-reviewed

Correlation is the degree to which two variables are related. Mathematically it is represented by 'r' -- Pearson's correlation coefficient. It is a number that ranges from -1 to +1, where -1 is a perfect negative correlation (one rises as the other falls), 0 is no correlation, and +1 is a perfect positive correlation (both rise and fall together). Correlation does NOT prove causation. Assuming one (at least partially) causes the other, the math simply provide no way to know. Either variable can be calculated from the other. For example, there is a correlation between education and income. Does increased education result in increased salaries (most people would say yes). However, do people with more money buy more education? That is almost certainly true as well. There can be very good correlations where neither cause the other. It may be that both are caused by some third variable. For example, there is a correlation between the price of Irish Whiskey and Catholic Priests' salara..

SAT Scores and Family Income

Much has been written about the relationship between SAT scores and test-takers’ family income. Generally speaking, the wealthier a student’s family is, the higher the SAT score.

Let’s take a look at how income correlated with scores this year. About two-thirds of test-takers voluntarily report their family incomes when they sit down to take the SAT. Using this information, the College Board breaks down the average scores for 10 income groups, each in a $20,000 range.

First, here are the individual test sections:

Source: College Board

Source: College Board

Source: College Board

Here are all three test sections next to each other (zoomed in on the vertical axis, so you can see the variation among income groups a little more clearly):

Source: College Board

A few observations:

	There’s a very strong positive correlation between income and test scores. (For the math geeks out there, the R² for each test average/income range chart is about 0.95.)
	On every test section, moving up an income category was associated with an average score boost of over 12 points.
	Moving from the second-highest income group and the highest income group seemed to show the biggest score boost. However, keep in mind the top income category is uncapped, so it includes a much broader spectrum of families by wealth.

Recently, a university surveyed recent graduates of the English Department for their starting salaries.?Recently, a university surveyed recent graduates of the English Department for their starting salaries. Four hundred graduates returned the survey. The average salary was $25,000 with a standard deviation of $2,500.

What is the best point estimate of the population mean?
A. $25,000
B. $2,500
C. 400
D. $62.5

What is the 95% confidence interval for the mean salary of all graduates from the English Department?
A. [$22,500, $27,500]
B. [$24,755, $25,245]
C. [$24,988, $25,012]
D. [$24,600, $25,600]2 years ago
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Best Answer - Chosen by VotersFirst question: A. $25,000
You are trying to estimate the mean, or average, of the population. The average for the sample is $25,000. For this problem, we should assume that the sample is representative of the population. The answer A, $25,000 out of the four choices is closest to the sample mean value $25,000.

Second question: B. [$24,755, $25,245]

Without a graphing calculator:

To find confidence intervals without a graphing calculator, you do have to plug it in the formula. The formula of a confidence interval for a mean where the sample standard deviation is:

sample mean ± (t-critical value) [sample standard deviation/√(sample size)]

Note that we are missing a piece of information: the t-critical value. To obtain the t-critical value, you must check a table. Your teacher will tell you where to find this table.
The t-critical value we will use for this problem is 1.649. The rest of the problem is just plugging your values in the formula. Note that you will get 2 values.

25,000 ± (1.649) [2500/√(400)]≈24754 or 25246
Since the boundaries of the confidence interval are 24754 and 25246, the closest answer is B, [$24,755, $25,245].

With a graphing calculator:

To obtain your confidence interval on a TI-83 graphing calculator, go to STATS, then to TESTS. Scroll down to TInterval. Enter your data, and press Enter on Calculate. The calculator will give you the interval of (24754, 25246). The closest answer is B, [$24,755, $25,245].
Note: If your teacher asks you to show the formula and its values despite the fact that you have a graphing calculator, you must use the invT( function, which is not present in all TI graphing calculators, or the table mentioned above. I have a TI-84+ Silver Edition, which came with this function. If you have this function in your TI graphing calculator, you may find it by going 2nd►DISTR and scrolling down. When you input your values, you use confidence level and degrees of freedom. To find the degrees of freedom, subtract 1 from the sample size.
invT(.95, 399)=1.648681473

What is the probability that the mean salary offer for these 80 students is 24,250 or less? The mean salary offered to students who are graduating from Coastal State University this year is $24,230, with a standard deviation of $3,712. A random sample of 80 Coastal State students graduating this year has been selected. What is the probability that the mean salary offer for these 80 students is 24,250 or less?

Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.

Can you explain this how to do this?

Examples of Confidence Interval Standard Deviation :A Random sample of 100 school teachers in a particular state has a mean salary of 31,578. It is knwon from the previous data that the standard deviation of the salaries of the teachers in the state is 4,415. Construct a 99% confidence interval estimate for the true mean salary for public school teachers for a given state.
Solution: Given α = 0.01, Zα/2 = 2.576, x¨= 31578, n=100 , σ = 4,415 and σx = σ / √n = 441.5
Thus the 99 percent confidence interval estimate for the mean salary, using the formula, is 31,578 ± 2.576 x 441.5 = 31,578 ± 1,137.3. That is we are 99 percent confident that the average salary of the public school teachers for the given state will be between 30,440.9 and 32,715.3.

IQ versus Income

SAT Scores and Family Income

The weekly salaries of teachers in one state are normally distributed w/ a mean of $490 and a Std. dvtn of $45

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