BackRandomization vs t Test Two samples of commute times from Boston and New York are randomly selected and it is found that the samples sizes are n1 = 18 and n2 = 12 and each of the two samples appears to be from a population with a distribution that is dramatically far from normal. Which method is more likely to yield better results for testing Mu1 is not equals to Mu2. Hypothesis test using the t distribution (as in Section 9-2) or the resampling method?
What conditions are necessary to use the t-test for testing the difference between two population means?
In a recent year, according to the Bureau of Labor Statistics, the median number of years that wage and salary employees had been with their current employer (called employee tenure) was 4.1 years. Information on employee tenure has been gathered since 1996 using the Current Population Survey (CPS), a monthly survey of about 60,000 households that provides information on employment, unemployment, earnings, demographics, and other characteristics of the U.S. population ages 16 and over. With respect to employee tenure, the questions measure how long employees have been with their current employers, not how long they plan to stay with their employers.
A congressional representative claims that the median tenure for employees from the representative’s district is less than the national median tenure of 4.1 years. The claim is based on the representative’s data, which is shown in the table at the right above. (Assume that the employees were randomly selected.)
a. Is it possible that the claim is true? What questions should you ask about how the data were collected?
Perform a hypothesis test with to see if there's evidence that .
No Variation in a Sample An experiment was conducted to test the effects of alcohol. Researchers measured the breath alcohol levels for a treatment group of people who drank ethanol and another group given a placebo. The results are given below (based on data from “Effects of Alcohol Intoxication on Risk Taking, Strategy, and Error Rate in Visuomotor Performance,” by Streufert et al., Journal of Applied Psychology, Vol. 77, No. 4). Use a 0.05 significance level to test the claim that the two sample groups come from populations with the same mean.
Blue Crabs A marine researcher claims that the stomachs of blue crabs from one location contain more fish than the stomachs of blue crabs from another location. The stomach contents of a sample of 25 blue crabs from Location A contain a mean of 320 milligrams of fish and a standard deviation of 60 milligrams. The stomach contents of a sample of 15 blue crabs from Location B contain a mean of 280 milligrams of fish and a standard deviation of 80 milligrams. At , α= 0.01can you support the marine researcher’s claim? Assume the population variances are equal.
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
Researchers are comparing the average number of hours worked per week by employees at two different companies. Below are the results from two independent random samples. Assuming population standard deviations are unknown and unequal, calculate the -score for the difference in means, but do not find a -value or state a conclusion.
Company A: ; hours; hours
Company B: hours; hours
A researcher is comparing average number of hours spelt per night by college students who work part-time versus those who don't. From survey data, they calculate hours and hours with a margin of error of 0.41. Should they reject or fail to reject the claim that there is no difference in hours slept between the two groups?
In Exercises 11–14, test the claim about the difference between two population means and at the level of significance . Assume the samples are random and independent, and the populations are normally distributed.
Claim: μ1<μ2; α=0.03
Population statistics:σ1=136 and σ2=215
Sample Statistics: x̅1=5004, n1=144, x̅2=4895, n2=156
Independent Samples Which of the following involve independent samples?
c. Data Set 1 “Body Data” includes a sample of pulse rates of 147 women and a sample of pulse rates of 153 men.
Independent and Dependent Samples In Exercises 5–8, classify the two samples as independent or dependent and justify your answer.
Sample 1: The IQ scores of 60 females
Sample 2: The IQ scores of 60 males
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?
Testing the Difference Between Two Means In Exercises 15–24, (a) identify the claim and state Ho and Ha, (b) find the critical value(s) and identify the rejection region(s), (c) find the standardized test statistic z, (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.
ACT English and Reading Scores The mean ACT English score for 120 high school students is 19.9. Assume the population standard deviation is 7.2. The mean ACT reading score for 150 high school students is 21.2. Assume the population standard deviation is 7.1. At α=0.10, can you support the claim that ACT reading scores are higher than ACT English scores? (Source: ACT, Inc.)
Find the critical value(s) for the alternative hypothesis, level of significance , and sample sizes and . Assume that the samples are random and independent, the populations are normally distributed, and the population variances are (a) equal and (b) not equal.
Ha:μ1>μ2 , α=0.01 , n1=12 , n2=15