3/5/2016 Chapter 6 Test 8. The diameters (in inches) of 17 randomly selected bol

Question

3/5/2016 Chapter 6 Test 8. The diameters (in inches) of 17 randomly selected bolts produced by a machine are listed. Use a 90% level of confidence to construct a confidence interval for (a) the population variance 2 and (b) the population standard deviation . Interpret the results. 4.473 4.418 4.0314.355 4.002 3.752 3.821 3.758 4.245 3.9614.113 4.571 3.946 3.7593.853 3.828 4.447 (a) The confidence interval for the population vanance is ( (Round to three decimal places as needed.) Interpret the results. Select the cormect choice below and fill in the answer box(es) to complete your choice (Round to three decimal places as needed.) O B. With 10% confidence, it can be said that the population variance is between 0 A. With 90% confidence, it can be said that the population variance is less than ° C. With 90% confidence, it can be said that D. With 10% confidence, it can be said that the population variance is greater than the population variance is between and (b) The confidence interval for the population standard deviation is ( (Round to three decimal places as needed.) Interpret the results. Select the cormect choice below and fill in the answer box(es) to complete your choice (Round to three decimal place as needed.) 0 A. With 10% confidence, you can say that C B. With 90% confidence, you can say that the population standard deviation is less than the population standard deviation is greater than inches inches ° C. With 10% confidence, you can say that D. With 90% confidence, you can say that the population standard deviation is between the population standard deviation is betweern and and inches inches 9. Use the confidence interval to find the margin of error and the sample mean. (0.728,0.830) The margin of error is The sample mean is 10. In a survey of 9000 women, 6431 say they change their nail polish once a week. Construct a 90% confidence interval for the population proportion of women who change their nail polish once a week. A 90% confidence interval for the population proportion is ( (Round to three decimal places as needed.) https:llxlitem prod.pearsoncmg.com/apiM1/print/math 5/9

Explanation / Answer

8.

A)

Using technology, the sample standard deviation is

s = 0.283436955

As              
              
df = n - 1 =    16          
alpha = (1 - confidence level)/2 =    0.05          
              
Then the critical values for chi^2 are              
              
chi^2(alpha/2) =    26.2962276          
chi^2(alpha/2) =    7.961645572          
              
Thus, as              
              
lower bound = (n - 1) s^2 / chi^2(alpha/2) =    0.048880932          
upper bound = (n - 1) s^2 / chi^2(1 - alpha/2) =    0.161447041          
              
Thus, the confidence interval for the variance is              
              
(   0.048880932   ,   0.161447041   ) [ANSWER]

***************************

OPTION C: with 90% confidence, it can be said that the populaito variance is between 0.049 and 0.161. [ANSWER]

********************************
              
b)

Also, for the standard deviation, getting the square root of the bounds,              
              
(   0.221090326   ,   0.40180473   )

*********************************

OPTION D: With 90% confidence, you can say that the population standard deviation is between 0.221 and 0.402. [ANSWER]

*******************************************

Hi! Please submit the next part as a separate question. That way we can continue helping you! Please indicate which parts are not yet solved when you submit. Thanks!

Related Questions

Navigate

• Browse (All)
• Browse 3
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.