Probability and Statistics (EEC338)Tutorial 021. (a) Consider an experiment in which a battery from a pack of 10 batteries istested using a multimeter until one with an acceptable voltage (S) isobtained. Let X be the number of batteries tested before the experimentterminates (one with an acceptable voltage (S) is obtained). List eachoutcome in the sample space along with the associated value of X.(b) Pa Endeley owns two petrol stations; one in Tiko with three pumps andanother in Buea with two pumps. The number of pumps in use at bothstations will be determined. Give the possible values for each of the followingrandom variables; T= the total number of pumps in useU= the difference between the numbers in use at both stationsV = the maximum number of pumps in use at either stationZ= the number of stations having exactly one pump use(c) The sample space for an experiment is S= {0, 1, 2, 5, 6}. List all possiblevalues of the following random variables:(i) X=2s (ii) X=5s² -1 (iii) X=cos (πS) (iv) X=(1-3s)-¹

Given:10 batteries are tested using a multimeter until one with an acceptable voltage(S).Find:Sample…

Answered: 1. (a) Consider an experiment in which…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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A random sample of n1 = 157 people ages 16 to 19 were taken from the island of Oahu, Hawaii, and 12 were found to be high school dropouts. Another random sample of n2 = 129 people ages 16 to 19 were taken from Sweetwater County, Wyoming, and 6 were found to be high school dropouts. Do these data indicate that the population proportion of high school dropouts on Oahu is different (either way) from that of Sweetwater County? Use a 1% level of significance. (a) What is the level of significance? What is the value of the sample test statistic? (Test the difference p1 − p2. Do not use rounded values. Round your final answer to two decimal places.) (c) Find (or estimate) the P-value. (Round your answer to four decimal places.)
The records of a light bulb manufacturer show that, when the manufacturing machinery is working correctly, the defect rate (due to imperfections in the material used) is 1%. The manufacturer's control department periodically tests samples of the bulbs, and when 1.25% or more are defective, they call repair technicians for service. The control department is going to take a random sample of 4400 light bulbs. Let p be the proportion of defective light bulbs in the sample assuming the machinery is working correctly. A) find the mean of p b)find the standard deviation of p c)Compute an approximation for P≥p0.0125, which is the probability that, assuming the machinery is working correctly, the repair technicians will be called. Round your answer to four decimal places.
The records of a light bulb manufacturer show that, when the manufacturing machinery is working correctly, the defect rate (due to imperfections in the material used) is 1%. The manufacturer's control department periodically tests samples of the bulbs, and when 1.25% or more are defective, they call repair technicians for service. The control department is going to take a random sample of 4400 light bulbs. Let p be the proportion of defective light bulbs in the sample assuming the machinery is working correctly. Answer the following. (If necessary, consult a list of formulas.) (a) Find the mean of p. (b) Find the standard deviation of p. (c) Compute an approximation for P(P ≥ 0.0125), which is the probability that, assuming the machinery is working correctly, the repair technicians will be called. Round your answer to four decimal places.
3. A researcher samples 5 colony of Species of K and 5 colonies of Species L, measures their sizes as: Species K Species L 4.7 5.3 5.2 4.6 6.1 4.1 5.8 4.8 5.2 4.2 а. Test if mean colony size of Species K and Species L are different from each other? Report a p-value. (You mav need to do an additional test to decide which test to apply for comparing the means) b. What is the power of the test in part a? С. The researcher would like to design a new experiment which will allow a two tailed hypothesis test with significance 0.05 and power 0.90. What should be the sample sizes nk and ni for Species K and Species L (use k = 1). %3D
In a study comparing banks in two countries, a sample of 142 matched pairs of banks was formed. Each pair contained one bank from country x and one from country y. The pairings were made in such a way that the two members were as similar as possible in regard to such factors as size and age. The ratio of total loans outstanding to total assets was calculated for each of the banks. For this ratio, the sample mean difference (country x - country y) was 0.0579, and the sample standard deviation of the differences was 0.3086. Test, against a two-sided alternative, the null hypothesis that the two population means are equal. (Assume α = 0.01.) Click the icon to view the critical values of the Student's t distribution. Which of the following correctly states Ho and H₁ ? A. Ho: Mx Hy = 0 H₁: Hx-Hy >0 OC. Ho: Mx Hy ‡0 Hi HxHy=0 - O E. Ho: Mx Hy = 0 H₁: Hx-Hy <0 B. Ho: Mx Hy = 0 H₁: Hx-Hy #0 D. Ho: Hx-Hy = 0 H₁: Hx-Hy 20 OF. Ho: Mx Hy = = 0 H₁: Hx-Hy ≤0
In a study comparing banks in two countries, a sample of 142 matched pairs of banks was formed. Each pair contained one bank from country x and one from country y. The pairings were made in such a way that the two members were as similar as possible in regard to such factors as size and age. The ratio of total loans outstanding to total assets was calculated for each of the banks. For this ratio, the sample mean difference (country x - country y) was 0.0579, and the sample standard deviation of the differences was 0.3086. Test, against a two-sided alternative, the null hypothesis that the two population means are equal. (Assume α = 0.01.) Click the icon to view the critical values of the Student's t distribution. The test statistic is t = 2.236. (Round to three decimal places as needed.) The critical value(s) is(are) (Round to three decimal places as needed. Use a comma to separate answers as needed.)
Is there an association between daily screen time and exercise habits in high school students? Mia selects a random sample of 123 high school students and categorizes them into 1 of 3 categories of screen time and whether they exercise. She would like to determine if there is convincing evidence of an association. Let = 0.05. What are the hypotheses for this test? H0: There is an association between daily screen time and exercise habits in high school students.Ha: There is no association between daily screen time and exercise habits in high school students.H0: There is no association between daily screen time and exercise habits in high school students.Ha: There is an association between daily screen time and exercise habits in high school students.H0: There is no difference in the distribution of daily screen time and exercise habits in high school students.Ha: There is a difference in the distribution of daily screen time and exercise habits in high school students.H0: There is a…
A random sample of n1 = 10 regions in New England gave the following violent crime rates (per million population). x1: New England Crime Rate 3.3 3.7 4.2 3.9 3.3 4.1 1.8 4.8 2.9 3.1 Another random sample of n2 = 12 regions in the Rocky Mountain states gave the following violent crime rates (per million population). x2: Rocky Mountain Crime Rate 3.9 4.1 4.5 5.5 3.3 4.8 3.5 2.4 3.1 3.5 5.2 2.8 Assume that the crime rate distribution is approximately normal in both regions. Do the data indicate that the violent crime rate in the Rocky Mountain region is higher than in New England? Use ? = 0.01. Solve the problem using both the traditional method and the P-value method. (Test the difference ?1 − ?2. Round the test statistic and critical value to three decimal places.) test statistic critical value
H6.
Use the data in the table below, which shows the employment status of individuals in a particular town by age group. Part-time Unemployed Age Full-time 0-17 25 187 252 18-25 391 200 199 26-34 434 66 22 35-49 562 192 149 50+ 461 170 237 If a person is randomly chosen from the town's population, what is the probability that the person is under 18 or employed part-time?
32)
6. As a researcher for an environmental agency, you have been asked to determine if the air quality in the Philippines has changed over the past 2 years. You select a random sample of 7 metropolitan cities and find the number of days each year that these cities failed to meet acceptable air quality standards. The results were given below. Can we conclude that after a year, there is no improvement in the air = 0.15. quality in the Philippines? Use a = City Year 1 Year 2 1 18 24 2 50 77 3 9 13 4 22 21 5 30 44 6 29 23 7 1 6

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