Scholastic Aptitude Test (SAT) mathematics scores of a random sample of 500 high

Question

Scholastic Aptitude Test (SAT) mathematics scores of a random sample of 500 high school seniors in the state of Texas are collected, and the sample mean and standard deviation are found to be 501and 112, respectively.

Question 1

Find a 95 % confidence interval on the mean SAT mathematics score for seniors in the state of Texas.

(refer to slides 8 & 9)

(500, 502)

(488.1, 513.9)

(491.2, 510.8)

(485, 517)

QUESTION 2

The contents of seven similar containers of sulfuric acid are 9.8, 10.2, 10.4, 9.8, 10.0, 10.2, and 9.6 liters. The sample mean is 10 and the sample standard deviation is 0.238. Find a 90% confidenceinterval for the mean contents of all such containers, assuming approximately normal distribution.

Refer to slides 5 and 6.

(9.83, 10.17)

(9.67, 10.33)

(9.74, 10.26)

(9.85, 10.15)

QUESTION 3

The contents of seven similar containers of sulfuric acid are 9.8, 10.2, 10.4, 9.8, 10.0, 10.2, and 9.6 liters. The sample mean is 10 and the sample standard deviation is 0.238. Find a 99% confidenceinterval for the mean contents of all such containers, assuming approximately normal distribution. Refer to slides 5 and 6.

(9.67, 10.33)

(9.74,10.26)

(9.77, 10.23)

(9.83,10.17)

(500, 502)

(488.1, 513.9)

(491.2, 510.8)

(485, 517)

Explanation / Answer

Kindly post 1 Qn at a time. I will post answer to the 1st Qn here:

Q1)

Params of normal dist are given in the Qn:

n = 500
Sample mean =501
Deviation = 112

1)

The 95% Ci is given by:

Sample mean +/- Z*Sigma/sqrt(N)
=501+-1.96*112/SQRT(500)

=491.2 TO 510.8

Answer is C

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