Hello,

I am struggling to understand how to find confidence intervals & p-values. Please show work on these problems so that I can use that to solve the rest of my homework!

Thank you.

Many food products contaln small quantltles of subslanoes mat would glye an undesireahle taste or smell If they are present In large amounts. An example Is the "off-odors" caused by sulfur compounds In wlne. Oenologlsts [wine experts] have determlned the odor threshold. the lowest oonoentratlon of a compound that d1e human nose can detect. For exam pler the odor threshold for dlmethyl sulde {DMS} ls given In the oenology literature as 25 mlcrograms per llter of wine {ugfl}. Llnlrained noses may be less sensldue, however. Here are the DIME odor thresholds for 10 beginnlng students of oenology. 35 32 3E] 33 24 40 26 21 31 36 Assume {this Is not reallstlc) that the standard deviatlon of the odor threshold for untrained noses is known to be a = 1" ugy'l. [a) Make a stemplot to 1lrerll'y that the distrlhutlon ls roughly symmetrle wlth no outliers. [A normal quantlle plot oonrms that there are no systemadr: departures from normallty. Enter numbers from smallest to largest, separated by spaces. Enter NDNE for stems wlth no values.) 2 2 [o] Glue a 95% oonoenoe interval for the mean DIME odor threshold among all hegln nlng oenologyI students. (Round your answers to three decimal places.) ( . l [o] Are you oonylnoed that the mean odor threshold for beglnnlng students ls hlgher than the published mreshold, 25 pgfl? Carry out a slgnlcanoe test to justlfy your answer. {Use a = I105. Round your value for 2 to two declmal plaoes and round your P-yalue to four declmal plaoes.) z = P-yalue = A smdy of me pay of corporate chlef esecutlye ofcers [CEOs]: esamlned the Increase In cash com pensaon of the CEDs of 9? companles, adjusted for Ination, in a recent year. The mean Increase In real compensation was J? = 6.9%, and the standard deviation of the Increases was s = 411%. Is this good euldence that 1e mean real compensation pl of all CECIs increased that year? \"Q: p = I} {no Increase} Hal p a El- {an increase) Because the sample size is Ia nge, the sample 5' Is close to the pcpulatlon or, so take or = 40%. [a] Sketch the normal nurse for the sampling distrllJutlon of} when HE, is true. Shade the area that represents the Pvalue for the cbsenred outcome A? = 6.9%. (Do this on paper. Your Instructor may aslc 1pm to turn In tl'IIs work.) [In] Calculate the Pyalue. [Round your answer to four declmal places.) [o] Is 1e result signicant at the a = 0.05 level? Do you think the study glues le'c-ng euldence that 1e mean compensalion of all CEOs went up? - Reject the null hypothesis. there is slgnlt'ant eyldence that the mean compensatlon of all CEOs went up. - Reect the null hypothesis. there is not slgnlcant eyldence that the mean oompensatlon of all CEOs went up. - Fall to reject the null hypothesls, there Is not slgnlflt'a nt evidence that the mean compensatlon of all CECE. went up. - Fall to reject the null hypothesis, there Is signicant evidence that the mean compensation of all CEDs went up. A Study of mess on me mmpus of your university reported a mean stress level of F6 {on a U to mo scale wlth a higher score Indlcatlng more su'ess} wlth a margln of error of 4 for 95% condence. The study was based on a random sample of 64 undergraduates. [a} lee the 95% condence Interval. I I [b] If 1.I'ou wanted 99% condence for me same study, would your margln of error be greater thanI equal to, or less than 4? Explain your answer. - It Is Imposslole to determlne If the margln of error wlll change uslng the Informatlon glven. - The new margln of error would be equal to 4. The margin of error wIII not change when the condence level Is Increased. - The new margln of error would be greater than 4. A larger margln of error ls needed to be more condent that the Interval Includes the true mean. - The condence level should never be changed for me same study. - The new margln of error would be less than 4. A smaller margln of error Is needed to be more condent that the interval includes the true mean. lr'nu Inlantto rent an unfurnished onebedroom apartment in Dallas next year. The mean monthly' rent fora random sample of 14 apartments adversed ln the local newspaper ls 59m. Assume the monthly rents ln Dallas follnw a Normal dislrlbutlon wlm a standard deulaljon of $295. Find a 95% condence Interval for me mean monthly rent for unfurnlsned one-bedroom apartments available for rent ln [I'lls comm unity. {Rnund your answers to two declmal planes.) 3:4:J \fDo 1.I'arlous occu patlonal groups differ In thelr diets? A Brllish study of thls questlon compared 35 drivers and 65 conductors of London dou hledecker buses. The conductors' jobs requlre more physlcal attlvlty. The artlcle reportlng the sold}; glues the data as "Mean tlall'glI consumptlon :l: rm." Some of the study results appear below. Drivers conductors Total calories 2325 1: 14 2345 :I: 22 Alcohol {grams} I125 1 0.1 0.39- 1 0.12 [a] Glue J7 and s for each of the four sets of measurements. {Glue answers accurate to 3 declmal places.) Drlvers Tolal Calorles: I: = |:| = :I Drl'u'ers Alcohol: JT: = |:| = :I :onductors Total Calories: J? = |:| = :I Eonductors Alcohol: E = |:| 5 = :I [b] Is there slgnlflcant evldence at the 5% level that conductors ocnsu me more calorles per day than do drlvers? Use the conservative two- sample t method to nd the tsta'lislicJ and the degrees of freedom. [Round your answer for t to three declmal places.) an: Concluslon -' Reject HID. -- Do not reject Ho. [c] How slg nlf'lcant is the observed dlfferenoe In mean alcohol consumptlon? Use the conservative taro-sample 1' method to obtaln the tstadsljc. [Round your answer to three declmal places.) I = |:| Concluslon -' REjECt Ha. -- Do not reject H\". [d] Give a 95% conlldence Interval for the mean dallllr alcohol consu mptlon of London double-decker bus conductors. [Round your answers to three declmal places.) E|:|r|:|l [ej Glue a 99% condence lnteru'al for the dlfference ln mean dallv alcohol consumptlon for drluers and conductors. {conductors m|nus drlvers. Round your answers to three decimal places.) |:|r|:|