Let pi and p2 equal the respective proportion of male and female collegestudents who make their beds. We shall test the null hypothesis Ho P1 = P2 against thealternative hypothesis H1 : P1 < P2.(a) Define a critical region that has a significant level of a = 0.05.(b) If 27 out of 90 men and 51 out of 98 women made their beds on a particular Mondaymorning, calculate the value of the test statistic and give your conclusion.In a large bin of crocus bulbs it is claimed that 1/4 with produce yellow1/4 will produce white crocuses, and 1/2 will produce purple crocuses. If 40 bulbscrocuses,produce 6 yellow, 7 white, and 27 purple crocuses, would the claim be rejected?

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Answered: Let pi and p2 equal the respective…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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In Company X, the personnel department gives two aptitude tests to applicants. One measures verbal ability while the other measures quantitative ability. From many years of experience, the company has found that a person's verbal score Y1 is normally distributed with mean of 50 and standard deviation (stdev) of 10. The quantitative scores Y2 are also normally distributed with mean of 100 and stdev 20. Y1 and Y2 appear to be independent. A composite score, Y, is assigned to each applicant where: Y= 3Y1 + 2Y2.Applicants whose composite scores are below 375 are automatically rejected. What is the probability that a random applicant gets automatically rejected? If six applicants submit resumes, what are the chances that fewer than half will fail the screening test?
Find the z-score that defines α=0 .05 and α=.01 critical regions for a one-tail test? 8. Find the z-score that defines α=0 .05 and α=.01 critical regions for a two-tail test?
An airport official wants to prove that the proportion of delayed flights for Airline A (denoted as p1) is less than the proportion of delayed flights for Airline B (denoted as p2). Random samples for both airlines after a storm showed that 51 out of 200 flights for Airline A were delayed, while 60 out of 200 of Airline B's flights were delayed. The test statistic for this problem is -1.00. The p-value for the test statistic for this problem is: p = 0.0228 p = 0.0668 p = 0.3413 p = 0.1587
You are performing a right-tailed matched-pairs test with 9 pairs of data.If α=.005α=.005, find the critical value, to two decimal places.
According to a certain government agency for a large country, the proportion of fatal traffic accidents in the country in which the driver had a positive blood alcohol concentration (BAC) is 0.38. Suppose a random sample of 105 traffic fatalities in a certain region results in 51 that involved a positive BAC. Does the sample evidence suggest that the region has a higher proportion of traffic fatalities involving a positive BAC than the country at the a = 0.01 level of significance? Because npo (1 - Po 10, the sample size is 5% of the population size, and the sample the requirements for testing the hypothesis satisfied. (Round to one decimal place as needed.) can be reasonably assumed to be random, What are the null and alternative hypotheses? is given to be random, cannot be reasonably assumed to be random, Ho: versus H,: (Type integers or decimals. Do not round.) is given to not be random, Find the test statistic, zo. Z0 = (Round to two decimal places as needed.) Find the P-value.…
Show all your work Indicate clearly the methods you use, because you will be scored on the correctness of your methods as well as on the accuracy and completeness of your results and explanations. Researchers are studying two populations of sea turtles, In population D. 30 percent of the turties have a shell length greater than 2 feet. In population E. 20 percent of the turtles have a shell length greater than 2 feet. Froma random sample of 40 turtes selected from D.15 had a shell length greater than 2 feet. From a random sample of 60 turtles selected fromE. 11 had a shell length greater than 2 feet. Let pry represent the sample proportion for D, and let p represent the sample proportion for E (a)What is the value of the difference pryPr?Show your work. (b) What are the mean and standard deviation of the sampling distribution of the difference in sample proportions p P:? Show your work and label each value. (c) Can it be assumed that the sampling distribution of the difference of the…
Regulations from the Environmental Protection Agency say that soil used in play areas should not have lead levels that exceed a 400 parts per million (ppm). Before beginning construction at a new site, an agent will take a sample of soil and run a significance test on the mean lead level in the soil. If the mean lead level in the sample is significantly higher than 400 ppm, then the soil is deemed unsafe and construction cannot continue. Here are the hypotheses for this test: Ho : µ 400 ppm (soil is unsafe) (where u is the mean lead level in the soil at the new site). Which of the following would be a Type I error in this setting? Choose 1 answer: The soil is actually safe, and the sample result is below 400 ppm. so construction continues. The soil is actually safe, and the sample result is significantly higher than 400 ppm. so construction stops. The soil is actually unsafe, and the sample result is below 400 ppm, so construction continues. The soil is actually unsafe, and the sample…
A team of engineers at the research center of a car manufacturer performs crash tests to determine the proportion of times the cars' airbags fail to operate in a crash. With the airbag system's new modified design, the team expected to reduce the failed proportion to be below last year's proportion of 0.08. They decided to test HO: p = 0.08 versus Ha: p < 0.08, where p = the proportion of failed airbags during crash tests. If 300 crashes performed in the lab resulted in 18 failures, which of the following is the test statistic for this test?
A study of parental empathy for sensitivity cues and baby temperament (higher scores mean more empathy) was performed. Let x, be a random variable that represents the score of a mother on an empathy test (as regards her baby). Let x, be the empathy = 68.36. Another random sample of 31 fathers gave score of a father. A random sample of 37 mothers gave a sample mean of x, X, = 60.06. Assume that o, = 11.55 and o, = 11.45. (a) Let u, be the population mean of x, and let u, be the population mean of x,. Find a 99% confidence interval for u, - Hz. (Round your answers to two decimal places.) lower limit upper limit (b) Examine the confidence interval and explain what it means in the context of this problem. Does the confidence interval contain all positive, all negative, or both positive and negative numbers? What does this tell you about the relationship between average empathy scores for mothers compared with those for fathers at the 99% confidence level? Because the interval contains only…
The U.S. Geological Survey compiled historical data about Old Faithful Geyser (Yellowstone National Park) from 1870 to 1987. Let x1 be a random variable that represents the time interval (in minutes) between Old Faithful eruptions for the years 1948 to 1952. Based on 9520 observations, the sample mean interval was x1 = 62.8 minutes. Let x2 be a random variable that represents the time interval in minutes between Old Faithful eruptions for the years 1983 to 1987. Based on 23,117 observations, the sample mean time interval was x2 = 73.0 minutes. Historical data suggest that ?1 = 8.98 minutes and ?2 = 12.83 minutes. Let ?1 be the population mean of x1 and let ?2 be the population mean of x2. (a) Compute a 90% confidence interval for ?1 – ?2. (Use 2 decimal places.) lower limit upper limit (b) Comment on the meaning of the confidence interval in the context of this problem. Does the interval consist of positive numbers only? negative numbers only? a mix of positive and…
When only two treatments are involved, ANOVA and the Student’s t-test (Chapter 11) result in the same conclusions. Also, for computed test statistics, t2 = F. To demonstrate this relationship, use the following example. Fourteen randomly selected students enrolled in a history course were divided into two groups, one consisting of six students who took the course in the normal lecture format. The other group of eight students took the course in a distance format. At the end of the course, each group was examined with a 50-item test. The following is a list of the number correct for each of the two groups. Traditional Lecture Distance 36 45 31 35 40 45 34 35 33 45 38 36 43 41 a-1. Complete the ANOVA table. (Round your SS, MS, and F values to 2 decimal places and p-value, F crit to 4 decimal places.) Source of Variation SS df MS F p-value F crit Treatment 96.01 1 96.01 5.67 0.0350 Error 203.21 12 16.93 Total 299.21 13…
Executives of a supermarket chain are interested in the amount of time that customers spend in the stores during shopping trips. The mean shopping time, μ , spent by customers at the supermarkets has been reported to be 36 minutes, but executives hire a statistical consultant and ask her to determine whether it can be concluded that μ is greater than 36 minutes. The consultant plans to do a statistical test and collects a random sample of 50 shopping times at the supermarkets. Suppose that the population of shopping times at the supermarkets has a standard deviation of 16 minutes and that the consultant performs her hypothesis test using the 0.05 level of significance.

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