Redigera Visa Infoga Format Typsnitt Verktyg Tabell Fönster Hjälp Dokument3 | Au

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Redigera Visa Infoga Format Typsnitt Verktyg Tabell Fönster Hjälp Dokument3 | Aubrik 2 The control off sensor signals in the process industry is based on studying signal level and sensor noise of the sensor in operation without the sensor being affected. The signal level represents the measurement magnitude. For a given sensor, the measurement noise is suspected to be normally distributed 200 control measurements were carried out, where the level of measurement noise x was observed. The results are given in the table below with a grouping of noise levels in four subdivisions. Level XS -1 Number of measurements 41 53 59 47 0

Explanation / Answer

As mean = 0 and sd = sqrt(1.5) is given, we can calculate the expected number of measurement of noise by using the central limit theorem.

Now, using the above probabilities we can find the expected number of frequencies by multipying the respective probabilities and 200. We get the below table,

Test statistics, chi-square = sum((Oi - Ei)^2) = 62.5922

Critical value of chi-square for 0.05 significance level and df = 3 is 9.3484

As critical value is less than test statistics, we reject the null hypothesis. This means there are not significant evidence to conclude that the measurement noise has normal distribution N(0, 1.5)

Level Probabilities X<= -1 0.2071 -1 < x <= 0 0.2929 0 < x <= 1 0.2929 1 < x 0.2071

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