alkhodartariq162002 alkhodartariq162002
  • 14-06-2021
  • Computers and Technology
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the grade point average collected from a random sample of 150 students. assume that the population standard deviation is 0.78. find the margin of error if c = 0.98.

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MrRoyal
MrRoyal MrRoyal
  • 18-06-2021

Answer:

[tex]E = 14.81\%[/tex]

Explanation:

Given

[tex]n = 150[/tex]

[tex]\sigma = 0.78[/tex]

[tex]c = 0.98[/tex]

Required

The margin of error (E)

This is calculated as:

[tex]E = z * \frac{\sigma}{\sqrt{n}}[/tex]

When confidence level = 0.98 i.e. 98%

The z score is: 2.326

So, we have:

[tex]E = 2.326 * \frac{0.78}{\sqrt{150}}[/tex]

[tex]E = 2.326 * \frac{0.78}{12.247}[/tex]

[tex]E = \frac{2.326 *0.78}{12.247}[/tex]

[tex]E = \frac{1.81428}{12.247}[/tex]

[tex]E = 0.1481[/tex]

Express as percentage

[tex]E = 14.81\%[/tex]

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