Para La Situación Que Se Presenta a Continuación Determine: A)

8/14/2019 Para La Situacin Que Se Presenta a Continuacin Determine: A)

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Para la situacin que se presenta a continuacin determine:

a) Para cada grupo determine subjetivamente y objetivamente si los datosprovienen de una distribucin normal

b) Determine los intervalos de confianza para la media poblacional de cada grupoe interprtelo.

(Ejercicio 1.2-1 de Susan)

Se realiza un estudio para ayudar a comprender el efecto del fumar en los patronesdel sueo. La variable aleatoria considerada es X, el tiempo en minutos que setarda en quedarse dormido. Las muestras de fumadores y no fumadores producenestas observaciones sobre X:

NO FUMADORES FUMADORES

17.2 19.7 18.1 15.1 18.3 17.6

16.2 19.9 19.8 23.6 24.9 20.1

19.8 22.6 20.0 24.1 25.0 21.4

21.2 18.9 22.1 20.6 23.3 20.2

21.1 16.9 23.0 20.1 17.5 21.3

21.8 22.1 21.1 20.5 20.4 20.7

19.5 18.8 19.2 22.4 19.3 17.4

15.1 20.5 17.7 21.3 16.0 24.8

16.8 21.2 18.1 22.1 15.9 25.2

22.8 22.4 19.4 25.2 18.3 25.0

25.8 24.1 15.0 24.1 21.6 16.3

24.3 25.7 15.2 18.0 23.8 17.9

23.2 25.1 16.1 17.2 24.9 19.9

15.7 15.3 19.9 23.1 23.0 25.1

box plor para los fumadores

Para la situacin que se presenta a continuacin determine:

a) Para cada grupo determine subjetivamente y objetivamente si los datosprovienen de una distribucin normal

b) Determine los intervalos de confianza para la media poblacional de cada grupoe interprtelo.

(Ejercicio 1.2-1 de Susan)

Se realiza un estudio para ayudar a comprender el efecto del fumar en los patronesdel sueo. La variable aleatoria considerada es X, el tiempo en minutos que setarda en quedarse dormido. Las muestras de fumadores y no fumadores producenestas observaciones sobre X:

NO FUMADORES FUMADORES

17.2 19.7 18.1 15.1 18.3 17.6

16.2 19.9 19.8 23.6 24.9 20.1

19.8 22.6 20.0 24.1 25.0 21.4

21.2 18.9 22.1 20.6 23.3 20.2

21.1 16.9 23.0 20.1 17.5 21.3

21.8 22.1 21.1 20.5 20.4 20.7

19.5 18.8 19.2 22.4 19.3 17.4

15.1 20.5 17.7 21.3 16.0 24.8

16.8 21.2 18.1 22.1 15.9 25.2

22.8 22.4 19.4 25.2 18.3 25.0

25.8 24.1 15.0 24.1 21.6 16.3

24.3 25.7 15.2 18.0 23.8 17.9

23.2 25.1 16.1 17.2 24.9 19.9

15.7 15.3 19.9 23.1 23.0 25.1

box plor para los fumadores


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box plot no fumadores

diagrama de tallos y hojas para los no Fumadores


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diagrama de tallos y hojas paralos Fumadores

Histograma de frecuenciaspara no fumadores

Histograma de frecuenciaspara fumadores


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Figura grfico deprobabilidad normal para no fumadores

Figura grfico deprobabilidad normal para fumadores

FUMADORES

Tests for Normality for Fumadores

Computed Chi-Square goodness-of-fit statistic = 34,9048

P-Value = 0,00151847

Shapiro-Wilks W statistic = 0,891436

P-Value = 0,000540195

Z score for skewness = 0,324667

P-Value = 0,745429

Z score for kurtosis = -4,73776

P-Value = 0,00000216351

The StatAdvisor

This pane shows the results of several tests run to determine whether Fumadorescan be adequately modeled by a normal distribution. The chi-square test divides therange of Fumadores into 17 equally probable classes and compares the number ofobservations in each class to the number expected. The Shapiro-Wilks test is basedupon comparing the quantiles of the fitted normal distribution to the quantiles ofthe data. The standardized skewness test looks for lack of symmetry in the data.The standardized kurtosis test looks for distributional shape which is either flatteror more peaked than the normal distribution. The lowest P-value amongst the tests

performed equals 0,00000216351. Because the P-value for this test is less than0.01, we can reject the idea that Fumadores comes from a normal distribution with99% confidence.


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Goodness-of-Fit Tests for Fumadores

Chi-Square Test

-

Lower Upper Observed Expected

Limit Limit Frequency Frequency Chisquare

-

at or below 18,2857 15 10,88 1,5618,2857 20,4286 4 9,03 2,80

20,4286 22,5714 6 9,37 1,21

22,5714 24,7143 8 7,00 0,14

above 24,7143 9 5,73 1,87

-

Chi-Square = 7,57861 with 2 d.f. P-Value = 0,0226113

Estimated Kolmogorov statistic DPLUS = 0,120603

Estimated Kolmogorov statistic DMINUS = 0,123036

Estimated overall statistic DN = 0,123036

Approximate P-Value = 0,548441The StatAdvisor

This pane shows the results of tests run to determine whether Fumadores can beadequately modeled by a normal distribution. The chi-square test divides the rangeof Fumadores into nonoverlapping intervals and compares the number ofobservations in each class to the number expected based on the fitted distribution.The Kolmogorov-Smirnov test computes the maximum distance between thecumulative distribution of Fumadores and the CDF of the fitted normaldistribution. In this case, the maximum distance is 0,123036. The lowest P-valueamongst the tests performed equals 0,0226113. Because the P-value for this test is

less than 0.05, we can reject the idea that Fumadores comes from a normaldistribution with 95% confidence.

Analysis Summary

Data variable: Fumadores

42 values ranging from 15,0 to 25,8

Fitted normal distribution:

mean = 20,669

standard deviation = 3,68858

The StatAdvisor

This analysis shows the results of fitting a normal distribution to the data onFumadores. The estimated parameters of the fitted distribution are shown above.You can test whether the normal distribution fits the data adequately by selectingGoodness-of-Fit Tests from the list of Tabular Options. You can also assessvisually how well the normal distribution fits by selecting Frequency Histogramfrom the list of Graphical Options. Other options within the procedure allow you tocompute and display tail areas and critical values for the distribution. To select adifferent distribution, press the alternate mouse button and select Analysis Options.

NO FUMADORES

Tests for Normality for Nofumadore Computed Chi-Square goodness-of-fit statistic= 9,0


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P-Value = 0,831051

Shapiro-Wilks W statistic = 0,98561

P-Value = 0,923601

Z score for skewness = 0,0150372

P-Value = 0,987997

Z score for kurtosis = -0,0393252

P-Value = 0,968625The StatAdvisor

This pane shows the results of several tests run to determine whether Nofumadorecan be adequately modeled by a normal distribution.

The chi-square test divides the range of Nofumadore into 17 equally probableclasses and compares the number of observations in each class to the numberexpected. The Shapiro-Wilks test is based upon comparing the quantiles of thefitted normal distribution to the quantiles of the data. The standardized skewnesstest looks for lack of symmetry in the data. The standardized kurtosis test looks fordistributional shape which is either flatter or more peaked than the normaldistribution. The lowest P-value amongst the tests performed equals 0,831051Because the P-value for this test is greater than or equal to 0.10, we can not rejectthe idea that Nofumadore comes from a normal distribution with 90% or higherconfidence.

Goodness-of-Fit Tests for Nofumadore

Chi-Square Test

-

Lower Upper Observed Expected

Limit Limit Frequency Frequency Chisquare

-at or below 19,1429 11 12,82 0,26

19,1429 20,8571 15 12,19 0,65

20,8571 22,5714 9 10,25 0,15

above 22,5714 7 6,73 0,01

-

Chi-Square = 1,06938 with 1 d.f. P-Value = 0,301082

Estimated Kolmogorov statistic DPLUS = 0,0537465

Estimated Kolmogorov statistic DMINUS = 0,062176

Estimated overall statistic DN = 0,062176

Approximate P-Value = 0,996881The StatAdvisor

This pane shows the results of tests run to determine whether Nofumadore can beadequately modeled by a normal distribution. The chi-square test divides the rangeof Nofumadore into nonoverlapping intervals and compares the number ofobservations in each class to the number expected based on the fitted distribution.The Kolmogorov-Smirnov test computes the maximum distance between thecumulative distribution of Nofumadore and the CDF of the fitted normaldistribution. In this case, the maximum distance is 0,062176. The lowest P-valueamongst the tests performed equals 0,301082. Because the P-value for this test is

greater than or equal to 0.10, we can not reject the idea that Nofumadore comesfrom a normal distribution with 90% or higher confidence.


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Analysis Summary

Data variable: Nofumadore

42 values ranging from 15,1 to 25,0

Fitted normal distribution:

mean = 20,3048

standard deviation = 2,28227

The StatAdvisor

This analysis shows the results of fitting a normal distribution to the data onNofumadore. The estimated parameters of the fitted distribution are shown above.You can test whether the normal distribution fits the data adequately by selectingGoodness-of-Fit Tests from the list of Tabular Options. You can also assessvisually how well the normal distribution fits by selecting Frequency Histogramfrom the list of Graphical Options. Other options within the procedure allow you tocompute and display tail areas and critical values for the distribution. To select adifferent distribution, press the alternate mouse button and select Analysis Options.

2. Obtenga una muestra aleatoria de tamao 60 de una distribucin normal conmedia 83 y desviacin estndar 10.

3. Resuelva la siguiente situacin

En cierta pobalcin de primates, el volmen de la cavidad craneal se distribuyeaproximadamente norml con media 1200 cc y desviacin estndar

a) Hallar la probabilidad de que un miembro de la poblacin seleccionadoaleatoriamente tenga una cavidad craneal superior a 1400 cc.

b) Hallar P 1000 x 1050

c) Hallar P x 1060

d) Hallar P x 920

e) Hallar el punto Xo tal que el 20% de los primates tenga una cavidad cranealms pequea que Xo.

f) Hallar el punto Xo tal que el 10% de los primates tenga una cavidad cranealsuperior a Xo.

Para La Situación Que Se Presenta a Continuación Determine: A)

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