A hypothesis test is conducted at the .05 level of significance to test whether or not the population correlation is zero. If the sample consists of 25 observations and the correlation coefficient is 0.60, then what is the computed value of the test statistic?
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A. B. C. D. E.B
Using the t statistics, t = r* [sq. root of ((n-2)/(1-r_squared))]. t = r*[n-2/(1-r^2)]^0.5. So t = 0.6*[23/0.64]^0.5 = 3.60.
To compute the test statistic for the hypothesis test, we can use the formula:
t = (r * sqrt(n - 2)) / sqrt(1 - r^2),
where:
In this case, the sample size is given as 25, and the correlation coefficient is 0.60. Let's plug these values into the formula to calculate the test statistic:
t = (0.60 * sqrt(25 - 2)) / sqrt(1 - 0.60^2) t = (0.60 * sqrt(23)) / sqrt(1 - 0.36) t = (0.60 * sqrt(23)) / sqrt(0.64) t = (0.60 * sqrt(23)) / 0.8 t = 0.75 * sqrt(23)
Now, let's calculate the approximate value of sqrt(23) and multiply it by 0.75:
sqrt(23) ≈ 4.795 0.75 * 4.795 ≈ 3.596
Rounding the result to two decimal places, we get:
t ≈ 3.60
Therefore, the computed value of the test statistic is approximately 3.60. Therefore, the correct answer is option B: 3.60.