Respuesta :
Answer:
[tex]3.13<\sigma^2 < 4.91[/tex]
Step-by-step explanation:
We are given the following in the question:
Sample size, n = 67
Variance = 3.85
We have to find 80% confidence interval for the population variance of the weights.
Degree of freedom = 67 - 1 = 66
Level of significance = 0.2
Chi square critical value for lower tail =
[tex]\chi^2_{1-\frac{\alpha}{2}}= 51.770[/tex]
Chi square critical value for upper tail =
[tex]\chi^2_{\frac{\alpha}{2}}= 81.085[/tex]
80% confidence interval:
[tex]\dfrac{(n-1)S^2}{\chi^2_{\frac{\alpha}{2}}} < \sigma^2 < \dfrac{(n-1)S^2}{\chi^2_{1-\frac{\alpha}{2}}}[/tex]
Putting values, we get,
[tex]=\dfrac{(67-1)3.85}{81.085} < \sigma^2 < \dfrac{(67-1)3.85}{51.770}\\\\=3.13<\sigma^2 < 4.91[/tex]
Thus, (3.13,4.91) is the required 80% confidence interval for the population variance of the weights.
