X(t StatCrunch : Group Activity t × Review Homework YO Review Homework X ogle.co

Question

X(t StatCrunch : Group Activity t × Review Homework YO Review Homework X ogle.com/document/d/19h2h_dmZAroG Ra0YLcvRoymedAEpwZL2x8 1 Ssit nQE/edit# STA 261 Group Dec x Google Translate 2. Germaine takes the ACT and scores 26 on the math portion of the test. ACT math scores have a mean of 20.4 and a standard deviation of 4.9. Bernie takes the SAT and scores 680 on the mathematics part of the SAT. The distribution of SAT math scores have a mean of 514 and a standard deviation of 118. a. Assuming that both tests measure the same kind of ability, who has the better test score relative to the mean for the test? How do you know? Show calculations that back up how you know. b. For the SAT test, give the interval for which about 95% of the scores on the math portion of the test should fall.

Explanation / Answer

a)
we need to find z value for Germaine
x = 26 , mean = 20.4 , s = 4.9
By normal distribution formula,

z = (x - mean) / s
= ( 26 - 20.4) / 4.9
= 1.142

we need to find z value for Bernie
x = 680 , mean = 514 , s = 118
By normal distribution formula,

z = (x - mean) / s
= (680 - 514) / 118
= 1.406

Bernie has the better test score relative to the mean for the test because bernie has z value higher than the germaine.

b)

Hence required interval is (282.7242 , 745.2758 )

CI for 95% n 1 mean 514 z-value of 95% CI 1.9600 std. dev. 118 SE = std.dev./sqrt(n) 118.00000 ME = z*SE 231.27575 Lower Limit = Mean - ME 282.72425 Upper Limit = Mean + ME 745.27575 95% CI (282.7242 , 745.2758 )

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