The correct size of a nickel is 21.21 millimeters. Based on that, the data can b

Question

The correct size of a nickel is 21.21 millimeters. Based on that, the data can be summarized into the following table: The coin size data (measured in millimeters) collected from each group is Too SmallToo Large Total Low Income High Income Total 19 21 21 shown below 35 75 35 Low Income High Income 24 24 21 25 21 16 For children in the low income group, find a 90% confidence interval for the proportion of children that drew the nickel too large. Give all answers correct to 3 decimal places. a) Critical valuc (positive valuc only) b) Margin of error: c) Confidencc intcrval: d) Does the confidence interval support the claim that more than 40% of children from the low income group draw nickels too large? 25 27 27 27 39 Preview 20 21 25 Confidence interval supports claim Confidence interval docs not support claim 21 12 20 19 19 25 17 For the high income group, find a 98% confidence interval for the mean nickel diameter c) Critical value (positive value only) f) Margin of crror: g) Confidence interval h) Does the confidence interval support the claim that average nickel size drawn by children from the high income is less than 22 mm? 28 28 25 Previcw 27 20 13 27 21 23 27 21 27 Confidence interval supports cla Confidence interval does not support claim im

Explanation / Answer

p = 21/40 = 0.525 , n = 40

a)
Critical value for 90% = 1.64

b)
ME = +/-z * sqrt(p * ( 1 - p ) / n)
= +/- 1.64 * sqrt( 0.525 * 0.475 / 40)
= 0.1295
c)
CI = p +/- ME
= 0.525 +/- 0.1295
= 0.3955 , 0.6545

Lower Bound = 0.3955
Upper Bound = 0.6545

Confidence interval: 0.3955 < p < 0.6545

mean = 20.5429 , s= 4.0245, sn = 35

e)
Critical value for 98% = 2.33

f)
ME= +/-z * ( s/sqrt(n))
= +/- 2.33 * ( 4.0245 /sqrt(35))
= 1.5850

g)
CI = mean +/- ME
= 20.5429 +/- 1.5850
= 18.9578 , 22.1279
Lower Bound = 18.9578
Upper Bound = 22.1279

Confidence interval: 18.9578 < mu < 22.1279

h)Confidence interval supports the claim

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