Question

A doctor claims that the standard deviation of systolic blood pressure is 12 mmhg. A random sample of 24 patients found a standard deviation of 14 mmhg. Assume the variable is normally distributed. At alpha=0.01, what are the critical χ2 values?

1) 13.848 and 36.415
2) 9.262 and 44.181
3) 13.091 and 35.172
4) 11.524 and 44.314

Answer 1

The critical chi-square values at a 0.01 significance level with 23 degrees of freedom are 9.262 and 44.181, matching option 2.

Step-by-step explanation:

The question is about using the chi-square (χ²) distribution to find the critical values for a given level of significance when testing a claim about a population standard deviation. In this case, the student is asked to determine the critical χ² values for a sample standard deviation of systolic blood pressure with a sample size of 24 and a significance level (alpha) of 0.01. The degrees of freedom for the chi-square distribution is the sample size minus one, which would be 23.

The critical values are determined by looking up the alpha/2 and 1 - alpha/2 quantiles in the chi-square distribution table or using statistical software. For alpha = 0.01 and 23 degrees of freedom, these values are:

• Lower critical value (χ² lower) = 9.260
• Upper critical value (χ² upper) = 44.181

Therefore, the correct critical values to answer the student's question are 9.262 and 44.181. Option 2 is the correct answer.