Statistics Chi Square test of normally distributed data

[Liesl]

Homework Statement

The following data is hypothesized to possesses a normal distribution, is that hypothesis sustained by a Chi-square test at .05 significance:

<66...4
67-68...24
68-70...35
70-72...15
72-74...8
>74...4

The Attempt at a Solution

1. I know that I should calculate the expected values for each bin for a normally distributed data set using the equation f(x)=2.66*e^-[(x-μ)^2/(2σ^2)] To do this, I'lll need to calculate μ and s from the data using estimators.

2. Then I can simply plug those values into the Chi Squared equation and see if the resulting value is less than the X^2 value from the table. (I will have to make sure np > 5 for all bins, and subtract 2 from the number of final bins to get the degrees of freedom).

My question is, how do is use estimators when the data is continuously distributed in bins as it is in the problem? Thank you.

 

[mfb]

I would try to minimize that Chi-squared value in a fit to get mean and standard deviation (and Chi2) at the same time.

 

[Ray Vickson]

Homework Statement

The following data is hypothesized to possesses a normal distribution, is that hypothesis sustained by a Chi-square test at .05 significance:

<66...4
67-68...24
68-70...35
70-72...15
72-74...8
>74...4

The Attempt at a Solution

1. I know that I should calculate the expected values for each bin for a normally distributed data set using the equation f(x)=2.66*e^-[(x-μ)^2/(2σ^2)] To do this, I'lll need to calculate μ and s from the data using estimators.

2. Then I can simply plug those values into the Chi Squared equation and see if the resulting value is less than the X^2 value from the table. (I will have to make sure np > 5 for all bins, and subtract 2 from the number of final bins to get the degrees of freedom).

My question is, how do is use estimators when the data is continuously distributed in bins as it is in the problem? Thank you.

You calculate the bin probabilities in the usual way: $P\{ a < X < b\} = P\{ (a - \mu)/\sigma < Z < (b - \mu)/\sigma\}$, where $Z$ is a standard normal random variable (mean= 0, variance = 1). You need to use normal tables or a computer package, or something similar.