In testing H₀: $\rho$_s = 0 vs.H₁: $\rho$_s $\neq$ 0 when the sample size n 30,the test statistic is approximately normally distributed with mean 0 and standard deviation equal to: A) $$\sqrt { n }$$ B) $$\sqrt { n - 1 }$$ C) $$1 / \sqrt { n }$$ D) $$1 / \sqrt { n - 1 }$$

Question

In testing H₀: $\rho$_s = 0 vs.H₁: $\rho$_s $\neq$ 0 when the sample size n > 30,the test statistic is approximately normally distributed with mean 0 and standard deviation equal to: A) $$\sqrt { n }$$ B) $$\sqrt { n - 1 }$$ C) $$1 / \sqrt { n }$$ D) $$1 / \sqrt { n - 1 }$$

Quizplus · Accepted Answer

When the sample size is greater than 30, we can use the standard normal distribution to approximate the sampling distribution of the test statistic. The standard deviation of this distribution is equal to the population standard deviation divided by the square root of the sample size. In hypothesis testing, we usually do not know the population standard deviation and therefore we use the sample standard deviation as an estimate. The correction factor of n-1 is used to adjust for the loss of one degree of freedom when estimating the population standard deviation from the sample. Therefore, the standard deviation of the test statistic is given by 1/sqrt(n-1).

In Testing H0 ρ\rhoρ s = 0 Vs ρ\rhoρ s ≠\neq= 0 When the Sample Size N > 30,the Test Statistic

In Testing H₀ $\rho$ _s = 0 Vs $\rho$ _s $\neq$ 0 When the Sample Size N > 30,the Test Statistic