Question

6. For the following prompts, please identify which “world” you’re working in (large means, small means, or large proportions). Then, simply write down any “givens” you would need to complete a hypothesis significance test or confidence intervals (identify mu, Y-bar, n and s for means; identify pi, pi-hat, k and n for proportions). Finally, complete steps 2 and 3 of the significance test procedure (the state hypotheses and test statistic steps (remember, stating the test statistic simply involves indicating your intention to find a z or a t statistic).

a. Previous research into the amount of debt amassed by undergraduate students stipulates that student accrue $20 (in thousands). However, you believe this is no longer the case. You collect data on 73 undergraduate students and find a sample average debt of $43 (in thousands) with a standard deviation of $6 (in thousands).

b. Conventional wisdom holds that the number of women holding political office constitutes 57% of representation in Congress. However, you believe this conclusion is widely off base. You conduct your own investigation and find that, out of 535 elected congressional officials, only 106 identify as females.

c. You are doing a school project on the average number of ice cream cones elementary school classes eat during the spring semester. Conventional wisdom states that elementary school classes eat 15.5 ice cream cones on average in the spring. You survey a 4th grade classroom with 23 students and find that their sample mean is 18.3 cones with a standard deviation of 3.5 cones.

Answer 1

(large means) Given M = 20$ (In thousands na 73 ý sample meam) = 43 $ can thousands Sample standers deviation S = 6 $ (an thousands Nul hypothesis to M = 20 (& Thouses) Alternate hypothesis to M 720 & Thranes, populandian Soans and deviation is unknoum has. o we have sample standent dansation given home we will fallow t test statesic for the rest of hypothesis ý t sin z 43-20 61573 z 32-752 Decesion about well Nelle hybuthez's t = 32.752 > te=1.666 It is then Conclused that will hypothesis is rejected therefor there is enough evidence to claim that the population mean (M) greater than 20 at the significare lace level is Ooos Nore { level of significus corridas rule of thumb) 0.05 as

6 Large proportion I given: population proportion (Pi) z 57/100 20.57 na 535 ♡ k z 106 106 535 z 0 1981 Nell hypornens Ho: Ps = 0.57 ps 0.57 Alterate hypotheen the Z NO Spoli-po) in 0.1981 - 0.57. 10.57 (1050)/555 Z - 17-374 Decesion about well hypothers! Net zi - 17-379 < Z02-1.64 zt is then Conduded that null heypothers is rejected therefor there is enough evidence to claim that population posparnian ps is leas than to (o.57 ) at X 20.05 level of signifiane corsidendz 0.05 as rule of think? { Nore

© (larger neam) given: = 15.5 n23 ý (sample means a 18.3 sample Standard deviation S z 3.5 we will use t teas statienic for test of hypothers population because Standad deviation is unknown How M & 15-5 Null hypomene Aeternak heysotheard hii M 7 15.5 test Statistic t X - sin 183 - 155 = Decesian 3:5/123 3.838 about Null hypotheens: t- 3.8377 te=6717 {for df = 22 aut os} it is then conclused that the null hypothesis is rejected, enough evidence to claim that the population greater than 15-5 [Qod 20.05 considered as rule of themb] therefore there is mean