91影视

An experiment to compare the spreading rates of five brands of yellow interior latex paint available in a particular area used \(4\)gallons \(\left( {J = 4} \right)\)of each paint. The sample average spreading rates \(\left( {f{t^2}/gal} \right)\) for the five brands were \(\,{\overline x _{1.}} = 462.3,\,{\overline x _{2.}} = 512.8,\,{\overline x _{3.}} = 437.5,\,{\overline x _{4.}} = 469.3\,and\,\,{\overline x _{5.}} = 532.1\,\) the computed value of F was found to be significant at level \(\alpha = .05.\) with MSE= \(272.8\)use Tukey鈥檚 procedure to investigate significant differences in the true average spreading rates between brands.

In Exercise \(11\) suppose \({\overline x _{3.}} = 427.5.\) now which true average spreading rates differ significantly from one another? Be sure to use the method of underscoring to illustrate your conclusion, and write a paragraph summarizing your results.

In an experiment to compare the tensile strengths of different type of\({\bf{I = 5}}\) copper wire, \({\bf{J = 4}}\) samples of each type were used. The between-samples and within- sample estimates of \({{\bf{\sigma }}^{\bf{2}}}\) were computed as \({\bf{MS}}{{\bf{T}}_{\bf{r}}}{\bf{ = 2673}}{\bf{.3}}\) and respectively. Use the F test at level. to test \({{\bf{H}}_{\bf{0}}}\,{\bf{:}}\,\,{{\bf{\mu }}_{\bf{1}}}{\bf{ = }}{{\bf{\mu }}_{\bf{2}}}{\bf{ = }}{{\bf{\mu }}_{\bf{3}}}{\bf{ = }}{{\bf{\mu }}_{\bf{4}}}{\bf{ = }}{{\bf{\mu }}_{\bf{5}}}\)versus \({{\bf{H}}_{\bf{a}}}{\bf{:}}\)at least two \({{\bf{\mu }}_{\bf{i}}}{\bf{'s}}\) are unequal.

The following data refers to yield of tomatoes (kg/plot) for four different levels of salinity. Salinity level here refers to electrical conductivity (EC), where the chosen levels were EC = 1.6, 3.8, 6.0, and 10.2 nmhos/cm.

Use the F test at level\(\alpha \)=.05 to test for any differences in true average yield due to the different salinity levels.

Suppose the compression strength observation on the fourth type of box in Example \(10.1\)had been \(655.1,\,748.7,\,662.4,\,679.0,\,706.9,\,and\,640.0\) and (obtained by adding \(120\) to each previous \({x_{4j}}\)). Assuming no change in the remaining observations, carry out an F test with \(\alpha = 0.5.\)

In an experiment to compare the quality of four different brands of magnetic recording tape, five 2400-ft reels of each brand (A鈥揇) were selected and the number of flaws in each reel was determined.

It is believed that the number of flaws has approximately a Poisson distribution for each brand. Analyse the data at level .01 to see whether the expected number of flaws per reel is the same for each brand.

Cortisol is a hormone that plays an important role in mediating stress. There is growing awareness that exposure of outdoor workers to pollutants may impact cortisol levels. The article 鈥淧lasma Cortisol Concentration and Lifestyle in a Population of Outdoor Workers鈥� (Intl. J. of Envir. Health Res., 2011: 62鈥�71) reported on a study involving three groups of police officers: (1) traffic police (TP), (2) drivers (D), and (3) other duties (O). Here is summary data on cortisol concentration (ng/ml) for a subset of the officers who neither drank nor smoked.

Assuming that the standard assumptions for one-way ANOVA are satisfied, carry out a test at significance level .05 to decide whether true average cortisol concentration is different for the three groups. (Note: The investigators used more sophisticated statistical methodology (multiple regression) to assess the impact of age, length of employment, and drinking and smoking status on cortisol concentration; taking these factors into account, concentration appeared to be significantly higher in the TP group than in the other two groups.)

The lumen output was determined for each of \(I = 3\)different brands of light bulbs having the same wattage, with \(J = 8\) bulbs of each brand tested. The sums of squares were computed as \(SSE = 4773.3\,and\,SS{T_r} = 591.2.\)state hypothese of intrest (including word definitions of parameters),and use the F test of ANOVA \(\left( {\alpha = .05} \right)\)to decide whether there are any differences in true average lumen outputs among the three brands for this type of bulb by obtaining as much information as possible about the p-values.

The critical flicker frequency \(\left( {cff} \right)\) is the highest frequency at which a person can detect the flicker in a flickering light source. At frequencies above the cff, the light source appear to be continuous even though it is actually flickering. An investigation carried out to see whether true average cff depends on iris color yielded the following data (based on the article 鈥淭he Effects of Iris Color on Critical Flicker Frequency鈥�.

Iris color

\(n = 19,{x_{..}} = 508.3\)

1. State and test the relevant hypotheses at significance level\(.05\)(Hint:\(\sum {\sum {{x_{ij}}^2} = 13659.67,CF = 13598.36} \))
2. Investigate difference between iris colors with respect to mean cff.

it is common practice in many countries to destroy (shred)refrigerators at the end of their usefull lives.In this process material from insulating foam may be released into the atmosphere.The article 鈥淩elease of fluorocarbons from Insulation foam in Home Appliances During shredding鈥�(J.of the Air and waste Mgmt.Assoc.,2007:1452-1460)gave the following data on foam density(g/L)For each of two refrigerators produced by four different manufactures:

\(\begin{aligned}{l}1.30.4,\,29.2\,\,\,\,\,2.27.7,27.1\\3.27.1,24.8\,\,\,\,\,\,4.25.5,28.8\end{aligned}\)

Does it appear that true average foam density is not the same for all these manufacture?carry out an appropriate test of hypotheses by obtaining as much p-value information as possible,and summarize your analysis in an ANOVA table.