1 answer the the relevant excel formula when then place your answers in the cells when given are five observations for two variables, x and y 14 a. compute the 15 b use 4 decimals use 4 decimals the t test statistic for the correlation coefficient

Question Answer
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1 answer the the relevant excel formula when then place your answers in the cells when given are five observations for two variables, x and y 14 a. compute the 15 b use 4 decimals use 4 decimals the t test statistic for the correlation coefficient.

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Calculating the T-Test Statistic for Correlation Coefficient in Excel

To solve this problem, we need to calculate the t-test statistic to determine the significance of the correlation between two variables, x and y, based on five observations.

:light_bulb: FORMULA USED:

The formula for the t-test statistic for a correlation coefficient (r) is:

t = \frac{r\sqrt{n-2}}{\sqrt{1-r^2}}

Where:

  • r = Pearson Correlation Coefficient
  • n = Number of observations (Sample size)
  • n-2 = Degrees of freedom

:brain: SOLUTION STEPS:

Step 1 — Calculate the Correlation Coefficient (r)
In Excel, you first need the correlation value. Assuming your x values are in cells A2:A6 and y values are in B2:B6:
Excel Formula: =CORREL(A2:A6, B2:B6)
Let’s assume the calculated r is stored in cell C1.

Step 2 — Identify the Sample Size (n)
The problem states there are five observations.
n = 5
Degrees of Freedom (df) = n - 2 = 5 - 2 = 3.

Step 3 — Compute the T-Test Statistic
Using the formula provided above, you can combine everything into one Excel cell to get the final t-value.

Excel Formula for Cell 15b:
=(C1*SQRT(5-2))/SQRT(1-C1^2)
(Note: Replace C1 with the actual cell where your correlation coefficient is calculated.)

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:white_check_mark: ANSWER:
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To get the t-test statistic using 4 decimals, use the following combined formula in your target cell:
=ROUND((CORREL(A2:A6,B2:B6)*SQRT(5-2))/SQRT(1-CORREL(A2:A6,B2:B6)^2), 4)

:bullseye: KEY CONCEPTS:

1. Pearson Correlation (r)

  • Definition: A measure of the linear strength and direction between two variables.
  • In this problem: It serves as the effect size used to generate the t-score.

2. T-Test Statistic

  • Definition: A value used in hypothesis testing to determine if the relationship between variables is statistically significant.
  • In this problem: We use the t-distribution because the sample size is small (n < 30).

:warning: COMMON MISTAKES:

:cross_mark: Incorrect Degrees of Freedom

  • Wrong: Using n or n-1 in the square root.
  • Right: Always use n-2 for correlation t-tests.
  • Why it’s wrong: Two degrees of freedom are lost because we are estimating the parameters for two variables (x and y).

:cross_mark: Order of Operations

  • Wrong: Forgetting parentheses around 1-r^2 inside the square root.
  • Right: Ensure the denominator is written as SQRT(1-C1^2) to maintain mathematical accuracy.

Do you have the specific values for x and y so I can help you calculate the exact numerical result for your cells?