A student scores 60 on a mathematics test that has a mean of 54 and a standard deviation of 3 , and she scores 80 on a history test with a mean of 75 and a standard deviation of 2. On which test did she perform better?

Which is relatively better: a score of 85 on a psychology test or a score of 45 on an economics test? Scores on the psychology test have a mean of 90 and a standard deviation of 10. Scores on the economics test have a mean of 55 and a standard deviation of 5.

Test Scores Which is a better relative position, a score of $83$ on a geography test that has a mean of $72$ and a standard deviation of $6$ , or a score of $61$ on an accounting test that has a mean of $55$ and a standard deviation of $3.5$ ?

Let A = {1,2,3,4,5,6,7,8}$. Determine whether the permutation is even or odd.

(a)$\left(

$$\begin{array}{llllllll}1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\ 4 & 2 & 1 & 6 & 5 & 8 & 7 & 3\end{array}$$

\right)$

Pertain to critical values for a MannWhitney test. Determine the critical value(s) in each case. For a left-tailed or two-tailed test, you will also need the relation $M_{1-A}=n_1\left(n_1+n_2+1\right)-M_A$.

$n_1=8, n_2=9$; Significance level =0.05

a. Right-tailed test

b. Left-tailed test

c. Two-tailed test

Explain how the chi-square independence test differs from the chi-square homogeneity of proportions test.

A student took two national aptitude tests. The national average and standard deviation were 475 and 100, respectively, for the first test and 30 and 8, respectively, for the second test. The student scored 625 on the first test and 45 on the second test. Use z scores to determine on which exam the student performed better relative to the other test takers.

Explain the following: The Root Test.

Describe: The Limit Comparison Test.

Use the Comparison Test, the Limit Comparison Test, or the Integral Test to determine whether the series converges or diverges.

$\sum_{n=1}^{\infty} \frac{\ln n}{n^2}$ (Hint: $\ln n \leq 2 \sqrt{n}$ for $n \geq 1$ by Exercise 53 of Section 5.7.)

Describe: The Ratio Test

What is meant by the power of a test?

State whether the null hypothesis should be rejected on the basis of the given P-value.

a. P-value $=0.258, \alpha=0.05$, one-tailed test

b. P-value $=0.0684, \alpha=0.10$, two-tailed test

c. P-value $=0.0153, \alpha=0.01$, one-tailed test

d. P-value $=0.0232, \alpha=0.05$, two-tailed test

e. P-value $=0.002, \alpha=0.01$, one-tailed test

What is meant by a statistical test?