a-university-claims-that-the-standard-deviation-of-the-scores-on-its-entrance-ex

Question

A university claims that the standard deviation of the scores on its entrance exam is at most 450450. State the null and alternative hypotheses. Which of the following best describes a Type I error in this context?

Accepted Answer

Null Hypothesis (H0):H0:σ≤450\left($$H_0$$\right):$$H_0$$:\sigma\le450Alternative Hypothesis 450"\u003e(Ha):Ha:σ\u003e450\left(H_{a}\right):H_{a}:\sigma\u003e450Concluding the standard deviation is greater than 450450 when it is actually at most 450450

Answer

Null Hypothesis 450 "\u003e(H0):H0:σ\u003e450 \left($$H_0$$\right):$$H_0$$:\sigma\u003e450 Alternative Hypothesis (Ha):Ha:σ≤450\left(H_{a}\right):H_{a}:\sigma\le450Concluding the standard deviation is greater than 450450 when it is actually at most 450450

Answer

Null Hypothesis (H0):H0:σ450\left($$H_0$$\right):$$H_0$$:\sigmaAlternative Hypothesis (Ha):Ha:σ≥450\left(H_{a}\right):H_{a}:\sigma\ge450Concluding the standard deviation is greater than 450450 when it is actually at most 450450

Answer

Null Hypothesis 450 "\u003e(H0):H0:σ\u003e450 \left($$H_0$$\right):$$H_0$$:\sigma\u003e450 Alternative Hypothesis (Ha):Ha:σ≤450\left(H_{a}\right):H_{a}:\sigma\le450Concluding the standard deviation is less than 450450 when it is actually at most 450450