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Mathematics & Economics

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# Statistics (Essay Sample)

Instructions:

A simple random sample of five months of sales data provided the following information
Develop a point estimate of the population standard deviation.
Let units sold be represented by X
The college board reported the following mean scores for three parts of the scholastic aptitude test (SAT) (The World Almanac, 2009):
Critical reading 502
Mathematics 515
Writing 494
Assume that the population standard deviation on each part of the test is 100
What is the probability a random sample of 90 test takers will provide a sample mean test score within 10 points of population means of 502 on the critical reading part of the test?
Therefore P(492 ) = 0.6578
What is the probability a random sample of 90 test taker will provide a sample mean test score within 10 points of the population mean of 515 on the mathematics part of the test?
It ranges in 10
What is the probability a random sample of 100 test taker will provide a sample mean test score within 10 points of the population mean of 494 on the writing part of the test?
It ranges in 10 source..

Content:

A simple random sample of five months of sales data provided the following information
Month
1
2
3
4
5
Units sold
94
100
85
94
92
Develop a point estimate of the population mean number of units sold per month.
Mean = units soldnumber of months = {94+100+85+94+92}5 = 4655 = 93
Develop a point estimate of the population standard deviation.
Let units sold be represented by x
x
(x-mean)
(x-mean)2
94
1
1
100
7
49
85
-8
64
94
1
1
92
-2
4
Standard deviation = (x-mean)2number of months-1 = (1+49+64+1+4)5-1 = 1164 = 29 = 5.3852
The college board reported the following mean scores for three parts of the scholastic aptitude test (SAT) (The World Almanac, 2009):
Critical reading 502
Mathematics 515
Writing 494
Assume that the population standard deviation on each part of the test is 100
What is the probability a random sample of 90 test takers will provide a sample mean test score within 10 points of population means of 502 on the critical reading part of the test?
It ranges in ±10
502 + 10 = 492
502 – 10 = 512
492≤502≤512
P(492≤502≤512 ) = P(502≤512)- P(502≤492) = P( Z ≤1010090) – P(Z ≤-1010090)
= P(Z≤0.95)- P(Z≤-0.95) = 0.8289 – 0.1711 = 0.6578
Therefore P(492≤502≤512 ) = 0.6578
What is the probability a random sample of 90 test taker will provide a sample mean test score within 10 points of the population mean of 515 on the mathematics part of the test?
It ranges in ±10
515 + 10 = 525
515...

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