10. Hypothesis Testing for Two Samples

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.

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 $\alpha =0.05$.

Create a confidence interval with $\alpha =0.1$ for the difference between the 2 population means to see if there's evidence that ${\mu }_1\ne {\mu }_2$.

"Walking in the Airport, Part I Do people walk faster in the airport when they are departing (getting on a plane) or when they are arriving (getting off a plane)? Researcher Seth B. Young measured the walking speed of travelers in San Francisco International Airport and Cleveland Hopkins International Airport. His findings are summarized in the table.

b. Explain why it is reasonable to use Welch’s t-test.

"

"[DATA] Measuring Reaction Time Researchers wanted to determine whether the reaction time (in seconds) of males differed from that of females to a go/no go stimulus. The researchers randomly selected 20 females and 15 males to participate in the study. The go/no go stimulus required the student to respond to a particular stimulus and not to respond to other stimuli. The results are as follows:

a. Is it reasonable to use Welch’s t-test? Why? Note: Normal probability plots indicate that the data are approximately normal and boxplots indicate that there are no outliers.