Question

Single Parameter Hypothesis Tests

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Question 1:

The shape of the Chi-squared distribution is controlled by the degrees of freedom parameter. we can use the confidence interval formula in the notes provided that we have a sample size n > 30 As the degrees of freedom increases, the Chi-squared distribution approaches a normal distribution. The Chi-squared distribution is symmetric The formula for a confidence interval for the variance of a population can be written

Question 2:

Answer 1

Note: Properties of the Χ² distribution:

1) It is not symmetric.

2) The shape depends on the degrees of freedom.

3) As the number of degrees of freedom increases, the distribution becomes more symmetric.

4) Χ²≥0

Question 1) Correct statements about the Chi-squared distribution:

i) The sahpe of the Chi-squared distribution is controlled by the degrees of freedom parameter.

ii) As the degrees of freedom increases, the Chi-squared distribution approaches a normal distribution.

Question 2) Correct statements about hypothesis testing

i) If the original claim involves equality, then it becomes the null hypothesis

ii) The wording of the final conclusion depends on whether the original claim was the null hypothesis or the alternative hypothesis.

iii) Hypothesis testing is used to test a claim about a population parameter.