hw6 - Find the critical value, 3;, neeessarjir ta farm a...

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Unformatted text preview: Find the critical value, 3;, neeessarjir ta farm a eenfidenee interval at the given level ef eenfidenee. e=|l96 zc= Reund tn the nearest hundredth. The level ef eenfidenee, e, is the middle area in the standard nermal eurve. Find 1 l thez-seere ewhere the area tn the left ef the z—seere is 3(1 - e} + :7, er 3 + 1 2:. Use the values en the number line tn find the sampling ermr. f: ltd. : The sampling errer is . Raund m the nwest hundredth The sampling errer is the differenee lf— lttl Find the margin ef errer fer the values efs, s, and n. s=fl.95,s=19,n=33 Calculate the margin ef ermr. _ s 3‘ Emeeu236,usethefermulaE=-Za . Raund tn the nearest hundredth. fl Match the level at" eanfidenee s with its representatien en the number line, given f = 6-4.6 , 5:5.6,E|11d H=4ll (a) (s3. 63.? 65.9 63.4 66 2 I IE64.§| ) x I :E 64.3 . A. 61 62 63 64 65 66 6’." 61 62 63 64 65 66 6'." (c) (a) 63.1 66.5 62 6 6TB E 64%| 3 . ' 64.3 . . -" .I.‘ 61 62 63 64 65 66 6'." 61 62 63 64 65 66 6'? Which graph ahnve enrrespends tn a eenfidenee level ef a: = [LEI]? Graph E (Type a, h, e, er d.) Find the difference between the f value and the endpoints. Solve the margin of error equation for z; and then match this value to the standard level of confidence values. 0' E = Z — fi fi Alternativelv, use the Elnterval function on a graphing calculator. Construct the indicated confidence interval for the population mean pi. s=|l§|9, f=ll.l,s=l.?,u=3? Choose the confidence interval for the population mean. Ga. “15:: p <11.3 Db. 9.4:: p. <12.E lIII.o-:: p: <11.s Gd. 1?: p <11.1 Determine the margin of error, E. Then add E to the sample mean to get the right endpoint of the confidence interval, and subtract E from the sample mean to get the left endpoint of the confidence interval. 5 E=2.';— fl Find the minimum sample size n needed to estimate pl for the given values of c, s, and E. c=fl.99,s=2??,E= 17" The minimum sample size is u = ITfil . (Round up to the next higher integer.) zc o- - E 1 Remember to round up to the next higher integer. Use the formula u = E . Since o' is unlmovm, estimate it using 5. A random sample of 3? premium hand tools has a mean price of $594.9? and a standard deviation of $59.99. Use this information to construct the 99% and 95% confidence intervals for the population mean. Which interval is wider? Construct the 99% confidence interval. (, (Round to the nearest hundredth.) Construct the 95% confidence interval. (, (Round to the nearest hundredth.) TWhich interval is wider, the 99% interval or the 95% interval? The as interval is wider. {Type an integer.) C" Use the equation E = z; E to find the sampling error. Suhtract this value from the sample mean price to find the left endpoint of the interval. Add this value to the sarnle mean rice to find the ri tend ' 0' Use the equation E = 2e E to find the sampling error. Subtract this value from the sample mean price to find the left endpoint of the interval. Add this value to the sample mean price to find the right endpoint. Find the difference hetween the two 99% endpoints and between the two 95% endpoints. Determine which value is greater. The confidence interval with the larger difference will he the wider interval. You work for a consumer advocate agency and want to find the mean repair cost of a certain ppliance. i—‘is part of your studpr vou randomlv select T9 repair costs and find the mean to he $199.99. The sample standard deviation is $31.69. Construct a 95% confidence interval for the I. opulation mean repair cost. Choose the 95% confidence interval for the population mean repair cost. @a. asses e e e sioew o 1:. $153.94 e e e sirsse c} c. ssieo e e e $131eo CI :1. resets e e $131eo C" Determine the margin of error using the formula E = 2; fl . i—‘idd E to the sample mean to get the right endpoint of the confidence interval, and suhtract E from the sample mean to get the left endpoint of the confidence interval. A random sample of 92 ofa certain plant has a mean height of T9 centimeters and a standard deviation of 17" centimeters. Construct a 95% confidence interval for the population mean height. Choose the 95% confidence interval for the population mean height, .tt . Ga. $3.1 cm: a «=: s31 cm Oh. 53.? cm-=: ltt <: 96.3 cm D c. all] cm: p: < 96.0 cm '3' d. T55 cmc: ltt c: 32.5 cm Recall that the left endpoint of the confidence interval is f— 35 or end ointisf+zc . p 1'11 r—‘iltemativelv, use the Zlnterval function on a graphing calculator. Find the critical value 1-} for the confidence level c and sample size n. c=|l95,n=19 What is the critical value? r.= (Round to the nearest thousandth.) Find the critical value I; for the confidence level c and sample size n. c=|].93,r1=29 What is the critical value”? r.= Find I; for n - 1 degrees of freedom. (Round to the nearest thousandth.) Find is for n - 1 degrees of freedom. In a random sample of 15 adults, the mean waste generated per pound per person per day is 4.9 pounds and the standard deviation is 1.2 pounds. Eissume the variable is nonnale distributed. Use a I-distribution or the normal distribution to construct a 95% confidence interval for the population mean .tt. Repeat the proeess assuming the statistics came from a sample size of 5E|E|. Find the 95% confidence interval for the population mean using sample size n = 15. t 1b, 1123' (Round to the nearest thousandth.) Find the 95% confidence level for the population mean Iv. using sample size n = 5|IIIII. (It, It) (Round to the nearest thousandth.) 5 Use the formula E = I; E to find the margin of error E for the sample data, Where I; is the critical value that corresponds to the desired confidence level and n - 1 degrees of freedom, 5 is the sample standard deviation, and n is the sample size. Use this to find the confidence interval. The left endpoint of the confidence interval is f - E, and the right endpoint is f + E. E=z {1.5 Let p be the population proportion for the given condition. Find point estimates for p and q. 999 randomly:r seleeted adults were surveyed, and 325 responded that they intend to spend more money this holiday season than last holidav seas on. TWhat is the point estimate for p? (Round to the nearest thousandth.) TWhat is the point estimate for q? (Round to the nearest thousandth.) The sample proportion in is the point estimate. it .9 = E , vvhere x is the number of successes and u is the number in the sample. The point estimate for the proportion of failures is r? = 1 — ,9. Let p he the population proportion for the given condition. Find point estimates for p and :3. Of so? children surveyed, 126 responded that they intend to hecome a teacher. What is the point estimate of p? (Round to the nearest thousandth.) What is the point estimate ofq‘? (Round to the nearest thousandth.) The sample proportion j: is the point estimate. 3: .3' = E , where x is the numher of successes and n is the sample size. The point estimate for the numher of failures is r? = 1 — E An election poll reported that a candidate had an approval rating of 52% with a margin of error E of 3%. Construct a confidence interval for the proportion of adults who approve of the candidate. Find the confidence interval. r, (Tvpe decimals. Round to the nearest hundredth.) A confidence interval for the population proportion p is (If? - E, f:- + E). Let p he the population proportion for the given condition. Construct a 95% confidence interval and a 99% confidence interval for the population proportion. lEEIEI randomly selected adults were surveyed, and 359 responded that the“):r intend to spend more monev this holiday season than last holiday season. f? = 9.299 and r? = |I|.7"|I|l. Write the 95% confidence interval for the population proportion. (, (Round to the nearest thousandth.) Write the 99% confidence interval for the population proportion. r, (Round to the nearest thousandth.) Use the formula for the margin of error. Then write the confidence interval E? - E sip <: j: + E. Use the formula for the magin of error. Then write the confidence interval f? - E sip <: j: + E. You are a travel agent and wish to estimate, with 00% confidence, the proportion of vacatioan who plan to travel to a certain region in the next 12 months. Your estimate must he accurate within 3% of the true proportion. Find the minimum sample size assuming It”? is not lo’roum. Then find the minimum sample size using a prior study that found 25% of the respondents said the}; plan to travel to that region in the next 12 months. Find the minimum sample size required assuming f? is not lmown. (Round up to the next higher integer.) Find the minimum sample size required using 25% as the population proportion estimate. (Round up to the next higher integer.) Substitute the assumed value of 0.5 for If? and if, 0.03 for E, and the z-score z :4 corresponding to a confidence level of 00% into the formula is = .3' If? . Remember to round up to the next higher integer. as E 2 J , using 0.25 for f? and thez-score Usetheformu]a,u=.5§'[ The table shows the results of a survey in Those in favor of the measure which 500 men and 500 women were Men 20% asked if the}; favored a certain measure. TWomen 17"% ISonstruct a 00% confidence interval for the proportion of men and the proportion of women who are in favor of the measure. Find the 00% confidence interval for the proportion of men who favor the measure. (, (Round to the nearest thousandth.) Find the 00% confidence interval for the proportion of women who favor the measure. (, (Round to the nearest thousandth.) Is it possible that the proportion for men and the proportion for women are equal? £1 a. Yes, the intervals overlap. D h. No, the intervals are not equal. 1'! If the confidence mtmrals nvarlap, the prop nrtinns could be equal. ...
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This note was uploaded on 04/01/2012 for the course MGQ 301 taught by Professor Orrange during the Fall '09 term at SUNY Buffalo.

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hw6 - Find the critical value, 3;, neeessarjir ta farm a...

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