Question

t a computer manufacturing company, the actual size of computer chips is normally distributed with a mean of 10 centimeter and a standard deviation of 2.1 centimeter. A random sample of 24 computer chips is taken. What is the probability that the sample 2. A mean will be between 10.95 and 11.05 centimeters? The personnel director of a large corporation wants to study absenteeism among clerical workers at the corporation's central office during the year. A random sample of 25 clerical workers reveals the following: 120 points Absenteeism: X-9.7 days, S-4.0 days. 12 clerical workers were absent more than 10 days. Set up a 95 % confidence interval estimate of the average number of absences for elerical workers last year. a. b. Set up a 95% confidence interval estimate of the population proportion of clerical workers absent more than 10 days last year. c. If the personnel director also wants to take a survey in a branch office, what sample size is needed if the director wants to be 95% confident of being correct to within t 1.5 days and the population standard deviation is assumed to be 4.5 days? d. If the personnel director also wants to take a survey in a branch office, what sample size is needed if the director wants to be 90% confident of being correct to within 0.075 of the population proportion of workers who are absent more than 10 days if no previous estimate is available? 3. Researchers determined that 80 tissues is the average number of tissues used during a cold. Suppose a random sample of 90 Kleenex users yielded the following data on the number of tissues used during a cold: X -50, Population standard deviation 4 a) Give the null and alternative hypotheses to determine if the number of tissues used during a cold is less than 55. b) Find the critical value if the level of significance to test the hypothesis is 0.05 c) Which table is appropriate Z or t? Explairn. 4. The quality control manager at a light bulb factory needs to determine whether the average life of a large shipment of light bulbs is equal to the specified value of 350 hours. The process standard deviation is known to be 80 hours. A random sample of 36 light bulbs indicates a sample mean life of 300 hours. At the 0.01 level of significance, is there evidence that the mean life is different from 350 hours? Answer the question by using all the steps of hypothesis testing.

Answer 1

92 chips (x)-Me101 noi PLO.as-10-ㄑㄧㄨ-사く1105-10 21424 A , pl 10.95 <×く 11-05), -Pl-2 . 216222くー2.4495) 0 ΟΙ 3339-一0.001153. = 0006186 Noor-X Sam 25 ct (d) ig ) _100[1-4% for o CI popth mean 24,0.0025 2.0639 a.7+ 2-0689 x 4 9:1-20639 x 4 25 25 (-8.0H8882ー11-35112) ire

b)-95% ст for 'populati (P) is 25 0-28 4 156863, 0- 61581 31372 a5%·フーg/ 0.05 (5%) Margin of eor- ME-1.5 ldle knouw 12 SD is б. 1.96x 4.55 88 ME 5.88- ME 0 015 O.1 0015 n = 120.0753 P 120

83 sSues usad -Hに 山< 55 cold is 55 SSues u Sample size n 9o Popudation Standard daviatian i8 koaun, we usili a z- test for testing tha hypathasis Caitical valueニー-Zd ス0.05 I : 645. = As mantionsd abaue, Sinca , the Sompla SizaI knouonz table will IS QH o test Mean life is 350 hous Mean ife ignot 350 hous Xe 300. population-SD a Sample sizo 80 σ-

Tost statistici Ze-u 300- 350 80 36 375 Citical value z 3 75 2.516 Decisi on ife is aiffunt hle conchuds thot tha fan 35o hus is sufficent evidanee to sup t the clain that 35o hus.