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Chrome File Edit View History Bookmarks People Window Help 100% " Sun Dec 24 2:59:17 PM Q E Take a Test- Payton Springle Secure l https://www.mathxl.com/Student/PlayerTest.aspx?testid=1732127078centerwin=yes Math 152 HIN (Holiday 2017) Payton Springle | 12/24/17 1:59 PM Test: Test 3 (Sections 6.1,6.2,7.1-7.4,9.1,9.2) Time Remalning: 00:14:41 Submit Te This Question: 1 pt 12 of 14 (12 complete) | This Test: 14 pts poss A soccer ball manufacturer wants to estimate the mean circumference of mini-soccer balls within 0.10 inch. Assume the population of circumferences is normally distributed. a Determine he minimum sample size required o construct a 99% confidence interval or the population mean. Assume he population standard deviation is .25 n . (b) Repeat part (a) using a population standard deviation of 0.35 inch. (c) Which standard deviation requires a larger sample size? Explain (a) The minimum sample size with a population standard deviation of 0.25 inch is balls Round up to the nearest integer.) (b) The minimum sample size with a population standard deviation of 0.35 inch is balls. (Round up to the nearest integer.) c A population standard deviation 0 inch requires a lar er sample size because greater varia i ity in the population requires a sample size to ensure the desired accuracy. Enter your answer in eech of the answer boxes. 24

Explanation / Answer

Z = (bar x – u) / (std deviation/ sqrt(n))

Thus, sqrt(n) = (z*std devistion)/ (bar x – u)

Given: (bar x – u)=0.10, Z = 2.58 (for 99% confidence interval)

a)std deviation = 0.25

Thus, sqrt(n) = 2.58*0.25/(0.1) = 6.45

n = (6.45)^2 = 41.60

Rounding off to 42

b)std deviation = 0.35

Thus, sqrt(n) = 2.58*0.35/(0.1) = 9.03

n = (9.03)^2 = 81.54

Rounding off to 82

c)Thus, population std deviation of 0.35 inch require larger sample size because greater variability in population requires a larger sample size to ensure the desired accuracy.

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