Performing a Wilcoxon Test In Exercises 3–8,
a. identify the claim and state H0 and Ha.
b. decide whether to use a Wilcoxon signed-rank test or a Wilcoxon rank sum test
c. find the critical value(s).
d. find the test statistic.
e. decide whether to reject or fail to reject the null hypothesis.
[APPLET] Earnings by Degree A college administrator claims that there is a difference in the earnings of people with bachelor’s degrees and those with advanced degrees. The table shows the earnings (in thousands of dollars) of a random sample of 11 people with bachelor’s degrees and 10 people with advanced degrees. At α = 0.01, is there enough evidence to support the administrator’s claim? (Adapted from U.S. Census Bureau)
Bachelor’s: 50, 63, 93, 69, 67, 99, 82, 67, 50, 74, 71
Advanced: 138, 88, 99, 113, 104, 102, 116, 84, 114, 96

In Exercises 17–20, (a) identify the claim and state H₀ and Hₐ, (b) find the critical value and identify the rejection region, (c) find the test statistic F, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim. Assume the samples are random and independent, and the populations are normally distributed.

[APPLET] An instructor claims that the variance of SAT evidence-based reading and writing scores is different than the variance of SAT math scores. The table shows the SAT evidence-based reading and writing scores for 12 randomly selected students and the SAT math scores for 12 randomly selected students. At α=0.01, can you support the instructor’s claim?

Take this quiz as you would take a quiz in class. After you are done, check your work against the answers given in the back of the book.For each exercise, perform the steps below.

a. Identify the claim and state Ho and Ha

b. Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed, and whether to use a z-test or a t-test. Explain your reasoning.

c. Find the critical value(s) and identify the rejection region(s).

d. Find the appropriate standardized test statistic.

e. Decide whether to reject or fail to reject the null hypothesis.

f. Interpret the decision in the context of the original claim.

[APPLET] The table shows the credit scores for 12 randomly selected adults who are considered high-risk borrowers before and two years after they attend a personal finance seminar. At α=0.01, is there enough evidence to support the claim that the personal finance seminar helps adults increase their credit scores? Assume the populations are normally distributed.

Test the claim about the difference between two population means and at the level of significance α. Assume the samples are random and independent, and the populations are normally distributed.

Claim: μ1≤μ2, α=0.05, Assume (σ1)^2≠(σ2)^2

Sample statistics:

x̅1=2410, s1=175, n1=13 and x̅2=2305, s2=52, n2=10

Test the claim about the difference between two population means and at the level of significance α. Assume the samples are random and independent, and the populations are normally distributed.

Claim: μ1=μ2, α=0.01, Assume (σ1)^2=(σ2)^2

Sample statistics:

x̅1=33.7, s1=3.5 , n1=12 and x̅2=35.5 , s2=2.2 , n2=17

[APPLET] Tensile Strength

The tensile strength of a metal is a measure of its ability to resist tearing when it is pulled lengthwise. An experimental method of treatment produced steel bars with the tensile strengths (in newtons per square millimeter) listed below.

Experimental Method:

391 383 333 378 368 401 339 376 366 348

The conventional method produced steel bars with the tensile strengths (in newtons per square millimeter) listed below.

Conventional Method:

362 382 368 398 381 391 400410 396 411 385 385 395 371

At , α=0.01 can you support the claim that the experimental method of treatment makes a difference in the tensile strength of steel bars? Assume the population variances are equal.

Difference in Means: Hypothesis Tests Using TI-84 Practice 2

For ${\bar{x}}_1=44,S_{x1}=2.3,n_1=50,{\bar{x}}_2=40,S_{x2}=3.1$, & $n_2=75$, test if there is evidence that ${\mu }_1>{\mu }_2$ for $\alpha =0.01$ using a hypothesis test.

Perform a hypothesis test with $\alpha =0.1$ to see if there's evidence that ${\mu }_1\ne {\mu }_2$.

For ${\bar{x}}_1=29,S_{x1}=3.3,n_1=40,{\bar{x}}_2=26,S_{x2}=3.8$, & $n_2=75$, create a confidence interval for the difference of the two means to test if there's evidence that ${\mu }_1>{\mu }_2$ for $\alpha =0.05$.