Consider a set of 50 measurements with mean 50.2 and standard deviation 18.7 and with the following observed and expected frequencies. It is desired to test whether these measurements came from a normal population.Calculate the value of the chi-square test statistic?
A)2.32
B)3.07
C)1.30
D)0.72

Question

Consider a set of 50 measurements with mean 50.2 and standard deviation 18.7 and with the following observed and expected frequencies.  It is desired to test whether these measurements came from a normal population.Calculate the value of the chi-square test statistic?
A)2.32 
B)3.07 
C)1.30 
D)0.72

Quizplus · Accepted Answer

To test whether the measurements came from a normal population, we use the chi-square goodness of fit test. The formula for the chi-square test statistic is:

χ² = ∑[(Oᵢ - Eᵢ)²/Eᵢ]

where Oᵢ is the observed frequency and Eᵢ is the expected frequency.

Using the observed and expected frequencies given in the table, we can calculate the chi-square test statistic as follows:

χ² = [(15-10.14)²/10.14] + [(8-10.14)²/10.14] + [(9-10.14)²/10.14] + [(7-10.14)²/10.14] + [(11-10.14)²/10.14]

χ² = 3.07

Looking at the answer choices, we see that the closest value to 3.07 is choice B. Therefore, the answer is B.

Consider a Set of 50 Measurements with Mean 50