Final answer:
To find the 95% confidence intervals for the variance and standard deviation of the lifetimes of wristwatches, we can use the chi-square distribution table. The chi-square value for a given alpha level (in this case, alpha = 0.05) is looked up in the table. The confidence interval for the variance is calculated using the formula (n-1)s^2 / X^2 21-alpha/2,n-1 and the confidence interval for the standard deviation is obtained by taking the square root of the lower and upper limits of the variance's confidence interval.
Step-by-step explanation:
To find the 95% confidence intervals for the variance and standard deviation, we can use the chi-square distribution table. For the variance, we can use the formula: (n-1)s^2 / X^2 21-alpha/2,n-1 and for the standard deviation, we can take the square root of the lower and upper limits of the confidence interval of the variance. First, we need to find the chi-square value for a given alpha level (in this case, alpha = 0.05).
For 95% confidence, the alpha level is 0.05. Looking up the chi-square value in the table for 29 degrees of freedom and an alpha level of 0.025 (because we want to find the two-tailed confidence interval), we find the chi-square value to be 45.723
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Using the formula, the confidence interval for the variance is ((n-1)s^2) / 45.723, ((n-1)s^2) / 14.449. Taking the square root of the lower and upper limits gives us the confidence interval for the standard deviation: sqrt(((n-1)s^2) / 45.723), sqrt(((n-1)s^2) / 14.449).