Physics High School

which assumption about level of measurement is made for the chi square test?

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Answer 1

The chi-square test assumes that the variables being analyzed are measured at a nominal or ordinal level of measurement.

In statistics, the level of measurement refers to the nature and properties of the data being collected. There are four levels of measurement: nominal, ordinal, interval, and ratio. Nominal and ordinal levels are considered categorical, while interval and ratio levels are considered numerical. The chi-square test is specifically designed for analyzing categorical data, where the observations can be classified into distinct categories or groups. It is used to determine whether there is a significant association or relationship between two categorical variables.

The test calculates the difference between the observed frequencies and the expected frequencies under the assumption of independence between the variables. It compares the observed and expected frequencies using a chi-square statistic and determines the p-value to assess the statistical significance of the association. Therefore, the chi-square test assumes that the variables being analyzed are measured at a nominal or ordinal level because it deals with categorical data and evaluates the relationship between different categories or groups.

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Related Questions

a 4700 kg railcar hits a bumper (a spring) at 1.9 m/s, and the spring compresses by 0.06 m. assume no damping.

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Given that a railcar of mass 4700 kg hits a bumper at 1.9 m/s and the spring compresses by 0.06 m, we are required to determine the force exerted by the spring on the railcar.

Using the formula for the force exerted by a spring, we get:F = kxwhereF = force exerted by the springk = spring constantx = compression of the springWe need to determine the spring constant k.To find the spring constant k, we use the formula,k = F / xWhere F is the force exerted by the spring and x is the distance by which the spring is compressed. In this case,x = 0.06 m, and the force exerted by the spring can be found as follows:The initial kinetic energy of the railcar is converted into elastic potential energy of the spring.

The total energy of the system is conserved, hence:1/2 mv² = 1/2 kx²wherev = 1.9 m/s (initial velocity)m = 4700 kg (mass of the railcar)x = 0.06 m (compression of the spring)k = spring constantRearranging the above formula, we can find k as,k = m v² / x²k = 4700 × 1.9² / 0.06²k = 5.872 × 10⁷ N/mNow that we have found the spring constant, we can use it to determine the force exerted by the spring:F = kx = 5.872 × 10⁷ × 0.06 = 3.523 × 10⁴ NTherefore, the force exerted by the spring on the railcar is 3.523 × 10⁴ N. Hence, F = 3.523 × 10⁴ N ,Here, we have made use of the spring formula which states thatF = kxwhereF = force exerted by the springk = spring constantx = compression of the springWe have determined the spring constant k ask = m v² / x²and then used it to find the force exerted by the spring on the railcar.

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find f , the magnitude of the force applied to each side of the nutcracker required to crack the nut. express the force in terms of fn , d , and d .

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To find the magnitude of the force applied to each side of the nutcracker required to crack the nut, we need to use the formula: F = (2Fn*d) / D.  where F is the required force, Fn is the force applied by each side of the nutcracker, d is the distance between the pivot point and the nut, and D is the distance between the pivot point and the point where the force is applied.

So, the magnitude of the force required to crack the nut can be expressed as F = (2Fn*d) / D. This formula shows that the magnitude of the force required to crack the nut is directly proportional to the force applied by each side of the nutcracker (Fn), and the distance between the pivot point and the nut (d), and inversely proportional to the distance between the pivot point and the point where the force is applied (D).

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