Question

Hn? 6. (16 poimts) In a rawlon sauke of 12 onuce swls cas the can volusnc is 11,9 ouuces with a stanulanl dr.viatim of culie. Tİc sanide sine 100 cius. Does the sample istovile couaviring evieleace that the mean voluane of 12 onuce soda cars is sanaller than 12 onsieCs? a. (4pts) State thhe unll hypothesis Ho and alteruntive eypothesis H. b. (4 pts) Ag Ho is trse, what is py? What value estimates ox d. (4pts) Bes ou the evis jurt, using, 05, do you reject or fail to rejoct 7. (16 points) Comsaler two inelepczudent randout saimpks of 400 boys and 900 girls. Of the boys, 200 reportel tlunt tleey listen to unsic at a ligh volnuue setting, Of the girls, 300 reported listesniug to utsi at a high volumc setting Perform a lyoteis test to deterunine if there is onvineiung evidenco that (in the pop- nlation) the proportion of lbugs elo listen to unsic at high volse is bigger than the pruportiou of girls wlo listes to wsáe at high volm a. (4 pts) State th will esás Ho nud alternntive hypotlcsis H let ph he the random varials for the proportion of lsys in a satuple of size 400 who listeu to mnsic at lhigh voluase. Let p, be tlhe ranlom varkalble ox the peoportiou of girk in a saunple of siee 900 who lesteu to nusic at high volnue -on) Assisti iaig Ho is tnie, find the prolal ility PG-P, 2 c● (4 pts) d. ( pts) Basel on tlhe peevikoses part usiug, 115, do yonu rejoct or fail to rejoct BONUS 8. (1e points) A randou saumple of five studeuts visiting the student hoalth center for a deutal exouninntion wire askol ow many nonthes lud passexd since their last visit to the deutist. Theis respouses werw as follows: 6,17, 11,22,29. Assuue that tlhe population distributiou is noruial. a. (4 pts) Caistrict iS 90% crnhlcune interval lor the nean niiber of months. elapad since the last visit to a dentist for the popmlation of stadents at the university b. (8 pts) Perforn a hypotlonis test to dcterninc if this sauple provides couvincing evidence that the nenn tinse hetwecu visits to the deut ist for stulents at the university is suore tlhan a year?

Answer 1

6)

(1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested Ho: μ = 12 Ha: μ < 12 This corresponds to a left-tailed test, for which a t-test for one mean, with unknown population standard deviation will be used (2) Rejection Region Based on the information provided, the significance level is α-0.05, and the critical value for a left- tailed test is te =-1.66. The rejection region for this left-tailed test is R = t : t <-1.66 The t-statistic is computed as follows: X- Ho 11.9 12 s/Vn 0.5/V100 (4) Decision about the null hypothesis Since it is observed that tーー2 < tcーー1.66, it is then concluded that the null hypothesis is using the P-value approach. The p-value is p = 0.0241, and since p = 0.0241 < 0.05, it is concluded that the null hypothesis is rejected. (5) Conclusion It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population mean μ is less than 12, at the 0.05 significance level.

a)

null and alternate hypothesis is in 1)

b)

mu_Xbar^ = sample mean = 11.9

sigma_Xbar = s/sqrt(n) = 0.5/sqrt(100) = 0.05

c)

P(Xbar < 11.9) = P(t < -2) = 0.0241

d)

p-value < alpha

we reject the null hypothesis