Questions: (c) determine the critical value in the table of critical values of the correlation coefficient to assess the normality of the data.

(c) determine the critical value in the table of critical values of the correlation coefficient to assess the normality of the data.
Transcript text: (c) determine the critical value in the table of critical values of the correlation coefficient to assess the normality of the data.
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Solution

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Solution Steps

Step 1: Identify the observed values and expected z-scores

The observed values and their corresponding expected z-scores are given in the data table. We will use these values to calculate the correlation coefficient.

Step 2: Calculate the correlation coefficient

The correlation coefficient, _r_, measures the linear relationship between the observed values and expected z-scores. While the exact formula can be complex, many calculators and software packages can calculate _r_ given two sets of data. Using the provided data:

Observed Value (x) | Expected Z-score (y) ------- | -------- 41 | -1.41 46 | -0.84 48 | -0.47 53 | -0.15 54 | 0.15 58 | 0.47 61 | 0.84 64 | 1.41

Using these values to calculate the correlation coefficient, we find _r_ ≈ 0.997.

Step 3: Round to three decimal places

The question asks for the correlation rounded to three decimal places. Since the calculated correlation is approximately 0.997, rounding to three decimal places gives 0.997.

Final Answer: The correlation is 0.997.

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