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Lifetimes of Wristwatches A random sample of the lifetimes of 29 inexpensive wristwatches has a standard deviation of 4.8 months. Assume the variable is normally distributed. Use the chi-square distribution table to find any chi-square values to three decimal places. Round your final answers to one decimal place. Part: 0/ 2 Part 1 of 2 Find the 98% confidence intervals for the variance and standard deviation.

Lifetimes of Wristwatches A random sample of the lifetimes of 29 inexpensive wristwatches has a standard deviation of 4.8 months. Assume the variable is normally distributed. Use the chi-square distribution table to find any chi-square values to three decimal places. Round your final answers to one decimal place. Part: 0/ 2 Part 1 of 2 Find the 98% confidence intervals for the variance and standard deviation.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
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Lifetimes of Wristwatches Find the 99% confidence interval for the variance and standard deviation for the lifetimes of inexpensive wristwatches if a sample of 23 watches has a standard deviation of 4.7 months. Assume the variable is normally distributed. Use the chi-square distribution table to find any chi-square values to three decimal places. Round your final answers to one decimal place. Do you feel that the lifetimes are relatively consistent? Explanation Formula for the Confidence Interval for a Variance (n – 1)s² (n – 1)s² Xieft d.f. =n-1 Since a= 0.01, the two critical values, respectively, for the 0.005 and 0.995 levels for 22 d.f. are Xnht = 42.796, n = 8.643 Xright The 99% confidence interval for the variance is found by substituting in the formula. (n – 1)s² (n- 1)s² <o? < Xieft (23 – 1)(4.7)² < g? < (23 – 1)(4.7)² 42.796 8.643 11.4 < o? < 56.2 Hence, you can be 99% confident that the true variance for the lifetimes of inexpensive wristwatches is between 11.4 and 56.2. For the standard deviation, the confidence interval is V11.4 < o < 56.2 3.4 < o< 7.5 Hence, you can be 99% confident that the true standard deviation for the lifetimes of inexpensive wristwatches is between 3.4 and 7.5 months, based on a sample of 23 wristwatches.
Transcribed Image Text:Lifetimes of Wristwatches Find the 99% confidence interval for the variance and standard deviation for the lifetimes of inexpensive wristwatches if a sample of 23 watches has a standard deviation of 4.7 months. Assume the variable is normally distributed. Use the chi-square distribution table to find any chi-square values to three decimal places. Round your final answers to one decimal place. Do you feel that the lifetimes are relatively consistent? Explanation Formula for the Confidence Interval for a Variance (n – 1)s² (n – 1)s² Xieft d.f. =n-1 Since a= 0.01, the two critical values, respectively, for the 0.005 and 0.995 levels for 22 d.f. are Xnht = 42.796, n = 8.643 Xright The 99% confidence interval for the variance is found by substituting in the formula. (n – 1)s² (n- 1)s² <o? < Xieft (23 – 1)(4.7)² < g? < (23 – 1)(4.7)² 42.796 8.643 11.4 < o? < 56.2 Hence, you can be 99% confident that the true variance for the lifetimes of inexpensive wristwatches is between 11.4 and 56.2. For the standard deviation, the confidence interval is V11.4 < o < 56.2 3.4 < o< 7.5 Hence, you can be 99% confident that the true standard deviation for the lifetimes of inexpensive wristwatches is between 3.4 and 7.5 months, based on a sample of 23 wristwatches.
Lifetimes of Wristwatches A random sample of the lifetimes of 29 inexpensive wristwatches has a standard deviation of 4.8 months. Assume the variable is normally distributed. Use the chi-square distribution table to find any chi-square values to three decimal places. Round your final answers to one decimal place. Part: 0 / 2 Part 1 of 2 Find the 98% confidence intervals for the variance and standard deviation. <o<
Transcribed Image Text:Lifetimes of Wristwatches A random sample of the lifetimes of 29 inexpensive wristwatches has a standard deviation of 4.8 months. Assume the variable is normally distributed. Use the chi-square distribution table to find any chi-square values to three decimal places. Round your final answers to one decimal place. Part: 0 / 2 Part 1 of 2 Find the 98% confidence intervals for the variance and standard deviation. <o<
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