Question

Use the given information to find the number of degrees of freedom, the critical values and χ,, and the confidence interval estimate of σ. It is reasonable to assume that a simple random sample has been selected from a population with a normal distribution Platelet Counts of Women 90% confidence; n = 23, s = 65.6. Click the icon to view the table of Chi-Square critical values df= □ (Type a whole number.) 尤- (Round to three decimal places as needed.) XR (Round to three decimal places as needed.) The confidence interval estimate of σ is「…く (Round to one decimal place as needed.) Enter your answer in each of the answer boxes.

Answer 1

a) The degrees of freedom here are computed as:

df = n-1 = 22

b) Now for 90% confidence level and 22 degrees of freedom, we get from the chi square tables that:

$P( \chi^2_{22}< 33.92) = 0.95$

$P( \chi^2_{22}<12.34) = 0.05$

Therefore the critical values here are given as:

$\chi^2_L = 33.920$

$\chi^2_R = 12.340$

Now the confidence interval for the standard deviation here is computed as:

$65.6*\sqrt{\frac{22}{33.92}} < \sigma < 65.6*\sqrt{\frac{22}{12.34}}$

$52.8 < \sigma < 87.6$

Thisis the required confidence interval here.