282 Some Elementary Statistical Inferences15.92 16.58 17.57 16.75 17.28 17.32 17.51 17.58 18.26 17.87rival: 15.95 16.15 17.05 16.99 17.34 17.53 17.34 17.51 18.10 18.19
16.04 16.80 17.24 16.81 17.11 17.22 17.33 17.82 18.19 17.88(a)Obtain comparison boxplots of the data. Comment on the comparison plots.
Are there any outliers?(b)Compute the pairedt-test and obtain thep-value. Are the data significant at
the 5% level of significance?(c)Obtain a point estimate ofμdand a 95% confidence interval for it.(d)Conclude in terms of the problem.4.6.6.Verzani (2014), page 323, presented a data set concerning the effect that
different dosages of the drug AZT have on patients with HIV. The responses we
consider are the p24 antigen levels of HIV patients after their treatment with AZT.
Of the 20 HIV patients in the study, 10 were randomly assign the dosage of 300 mg
of AZT while the other 10 were assigned 600 mg. The hypotheses of interest are
H 0 :Δ=0versusH 1 :Δ =0whereΔ=μ 600 −μ 300 andμ 600 andμ 300 are the true
mean p24 antigen levels under dosages of 600 mg and 300 mg of AZT, respectively.
The data are given below but are also available in the fileaztdoses.rda.300 mg 284 279 289 292 287 295 285 279 306 298
600 mg 298 307 297 279 291 335 299 300 306 291(a)Obtain comparison boxplots of the data. Identify outliers by patient. Com-
ment on the comparison plots.(b)Compute the two-samplet-test and obtain thep-value. Are the data signifi-
cant at the 5% level of significance?(c)Obtain a point estimate of Δ and a 95% confidence interval for it.(d)Conclude in terms of the problem.4.6.7.Among the data collected for the World Health Organization air quality
monitoring project is a measure of suspended particles inμg/m^3 .LetXandYequal
the concentration of suspended particles inμg/m^3 in the city center (commercial
district) for Melbourne and Houston, respectively. Usingn=13observationsofX
andm=16observationsofY,wetestH 0 :μX=μY againstH 1 :μX<μY.
(a)Define the test statistic and critical region, assuming that the unknown vari-
ances are equal. Letα=0.05.(b)Ifx=72. 9 ,sx=25. 6 ,y=81.7, andsy=28.3, calculate the value of the
test statistic and state your conclusion.