Use the given information to find the number of degrees of freedom, the critical values xi and x', and the confidence interval estimate of 0'. It is reasonable to assume that a simple random sample has been selected from a population with a normal distribution. Nicotine in menthol cigarettes 90% condence; n = 24, s = 0.21 mg. 5 Click the icon to View the table of ChiSquare critical values. Use the given information to find the number of degrees of freedom, the critical values XE and X?! , and the condence interval estimate of a. It is reasonable to assume that a simple random sample has been selected from a population with a normal distribution. Nicotine in menthol cigarettes 98% condence; n =18, s= 0.27 mg. 1 Click the icon to view the table of ChiSquare critical values. In general, the number of degrees of freedom [or df] for a collection of sample data is the number of sample values that can vary after certain restrictions have been imposed on all data values. The number of degrees of freedom for the chisquare distribution is the sample size minus 1. For estimating a, rst nd the number of degrees of freedom. First' calculate the degrees of freedom. degrees of freedom = n -1 = 18 - 1 = 17 To nd the critical values of x2, rst determine the area needed in each tail of the chisquare distribution for the given condence level. Start by calculating the value of o. 98% = (1 cal-100% 0.98 = 1 - 0: Divide both sides by 100%. - 0.02 = - or Subtract 1 from both sides. 0.02 = 0: Multiply both sides by -1. To divide or equally between the two tails of the chisquare distribution, divide a by 2. ==o.01 2 2 Determine the critical values of x2 that must be found. 2_ 2 _ 2 XL'M-bm '1039 2 _ 2 JCR'Xom While either technology or a table can be used to nd the critical values of x2 with 17 degrees of freedom. for this problem, use technology, rounding to three decimal places. XE = x399 = 5.408 and ya = x301 = 33409 If using a table of ChiSquare critical values to nd If or KER and the table does not include the number of degrees of freedom, the next lower number of degrees of freedom found in the table could be used as a conservative value, the closest critical value in the table could be used, or the critical value could be approximated using interpolation. For numbers of degrees of freedom greater than 100, use the equation below, or use a more extensive table, or use technology. In the formula, 2M2 is the z score separating an area of NZ in the right tail of the standard normal distribution and k is the number of degrees of freedom. '1 legacymf While either technology or the formula below can be used to determine the limits of a condence interval for the population standard deviation 0, in this problem, use the formula. In the formula, n is the number of sample values, s is the sample standard deviation, 9;?! is the righttailed critical value of x2, and If is the lefttailed critical value of 3:2. hrlpsszxlite mprod.pearsoncmg .comtapifv l r'printx'highered \"3 11:15:22, 2:34 PM Hw IS (Sec 7.3)Yuqian Chen Substitute n =18, S: 0.27, x = 33.409, and x5 = 6.408 into the formula in the previous step, and simplify, rounding to two decimal places. 2 2 (18-0027