Question

1. True or False? A ChiSquare distribution and a normal distribution will always have the same shape?

2. What is the minimum value that a ChiSquare distribution can have?

3. Which ChiSquare distribution has a higher peak; One that has 15 degrees of freedom or one that has 5 degrees of freedom.

4. True or False?  If the differences between observed values and an expected values are small, you will get a large ChiSquare Statistic.

5. Explain in 4-6 sentences why it is necessary in some cases to apply a log transformation to random samples in order to execute or perform a hypothesis test.

6. Explain in 4-6 sentences what it means for a statistical test to be robust.

Answer 1

1) false

The shape of the chi square distribution is based on its df. Its shape is skewed to right.

When the df> 90 , then it's approximately normal.

2) since chi square distribution is not symmetric distribution (asymmetric) which is skewed to right the minimum value would be 0.

3) the chi square distribution with 15 degress of freedom has lower peak when compared to df with 5

Df with 5 have higher peak .

4) false

If the difference between the observed value and expected value is small then the chi square vale also small.