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To test for any significant difference in the number of hours between breakdowns for four machines, the following data were obtained. Machine 1 Machine 2 Machine 3 Machine 4 ------------ 6.7 8.8 10.9 9.9 8.0 7.5 10.0 12.8 5.6 9.5 9.5 12.0 7.7 10.3 9.9 10.7 8.8 9.2 8.8 11.3 7.6 9.9 8.5 11.7 (a) At the α=0.05 level of significance, what is the difference, if any, in the population mean times among the four machines? State the null and alternative hypotheses. H0: μ1=μ2=μ3=μ4 Ha: Not all the population means are equal. Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to three decimal places.) p-value = State your conclusion. - Do not reject H0. There is sufficient evidence to conclude that the mean time between breakdowns is not the same for the four machines. - Reject H0. There is sufficient evidence to conclude that the mean time between breakdowns is not the same for the four machines. - Do not reject H0. There is not sufficient evidence to conclude that the mean time between breakdowns is not the same for the four machines. - Reject H0. There is not sufficient evidence to conclude that the mean time between breakdowns is not the same for the four machines. (b) Use Fisher's LSD procedure to test for the equality of the means for machines 2 and 4. Use a 0.05 level of significance. Find the value of LSD. (Round your answer to two decimal places.) LSD= Find the pairwise absolute difference between sample means for machines 2 and 4. mean2-mean4 What conclusion can you draw after carrying out this test? - There is a significant difference between the means for machines 2 and 4. - There is not a significant difference between the means for machines 2 and 4.
SITUATION-PROBLÈME Le laboratoire informatique L'école veut actualiser son laboratoire informatique en achetant du nouveau matériel. Anaís doit planifier les achats nécessaires. Local Le local rectangulaire mesure 10 m sur 21,5 m. Des tables pouvant accueillir chacune trois ordinateurs occupent près de 40 % de l'espace. Sur l'une d'elles, on disposera deux imprimantes et aucun ordinateur. Les tables, déjà disponibles à l'école, ont la forme illustrée ci-contre. Matériel Deux modèles de moniteurs sont offerts. Anaïs doit choisir le modèle qui a la plus haute définition, La définition est le nombre de pixels ( px ) qui forment l'image affichée sur le moniteur. Description des moniteurs Moniteur A B Définition 4,74 × 10^6 px 4,4 Mpx Cout () 350 325 Dix ordinateurs se vendent 5615 . Ce prix comprend des frais fixes de livraison de 65 . Anaïs doit choisir deux logiciels parmi les suivants et les installer sur tous les ordinateurs. Pour un seul ordinateur: - L'abonnement à une suite bureautique coûte 85 /an; - L'abonnement à un modificateur de documents PDF coûte 21 /mois; - Le correcteur orthographique et grammatical coûte 130 , et aucun abonnement n'est nécessaire. Trois modèles d'imprimantes sont offerts. Anaïs doit choisir le modèle le plus performant, soit celui dont le temps d'impression pour un caractère est le plus court. Description des imprimantes Imprimante A B C Temps d'impression 5 × 10^-4 s / caractère 2,4 × 10^-2 s / 6 caractères 6 × 10^-1 s / 100 caractères Count () 655 725 690 Détermine le matériel à acheter et, sachant que toutes les taxes sont comprises dans les prix, le coût total pour un an de ces achats.
The following table shows the wind chill C(T, w) (in °F) as a function of the air temperature T (in °F) and the wind speed w (in miles per hour) according to the current National Weather Service model. 5 10 15 20 25 30 35 ------------------------ 40 36 34 32 30 29 28 28 35 31 27 25 24 23 22 21 30 25 21 19 17 16 15 14 T 19 15 13 11 9 8 7 25 13 9 6 4 3 1 0 15 7 3 0 -2 -4 -5 -7 10 1 -4 -7 -9 -11-12-14 There are three ways to estimate a partial derivative from a table of values, the forward difference quotient (for example, fx(a, b) approximates (f(a+h, b)-f(a, b))/h with h>0), the backward difference quotient (for example, fx(a, b) approximates (f(a, b)-f(a-h, b))/h with h>0), and the symmetric difference quotient (for example, fz(a, b) approximates (f(a+h, b)-f(a-h, b))/(2 h) with h>0). The symmetric difference quotient is just the average of the forward and backward difference quotients. The forward difference quotient approximation to CT(15,25) is °F / °F. The backward difference quotient approximation to CT(15,25) is °F / °F. The symmetric difference quotient approximation to CT(15,25) is °F / °F. The forward difference quotient approximation to Cw(15,25) is -0.2 °F / mph. The backward difference quotient approximation to Cw(15,25) is -0.4 °F / mph. The symmetric difference quotient approximation to Cw(15,25) is °F / mph. The National Weather Service has also provided an empirical formula for approximating the wind chill. It states that C(T, w) approximates 35.74+0.6215 T+w^(0.10)(-35.75+0.4275 T) Based on this formula, CT(15,25) approximates °F / °F and Cw(15,25) approximates °F / mph.