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Whitepunk [10]
3 years ago
9

A random sample of 49 statistics examinations was taken. the average score, in the sample, was 84 with a variance of 12.25. the

95% confidence interval for the average examination score of the population of the examinations is
Mathematics
1 answer:
tester [92]3 years ago
6 0

Since in this case we are only using the variance of the sample and not the variance of the real population, therefore we use the t statistic. The formula for the confidence interval is:

<span>CI = X ± t * s / sqrt(n)                      ---> 1</span>

Where,

X = the sample mean = 84

t = the t score which is obtained in the standard distribution tables at 95% confidence level

s = sample variance = 12.25

n = number of samples = 49

From the table at 95% confidence interval and degrees of freedom of 48 (DOF = n -1), the value of t is around:

t = 1.68

 

Therefore substituting the given values to equation 1:

CI = 84 ± 1.68 * 12.25 / sqrt(49)

CI = 84 ± 2.94

CI = 81.06, 86.94

 

<span>Therefore at 95% confidence level, the scores is from 81 to 87.</span>

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Please explain every step
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<h3>Answer:</h3>

761680

<h3>Explanation:</h3>

\sf \boxed{\sum _{n=1}^{44}\:60\left(1.2\right)^{n-2}}

<u>Identify the following's</u>:

First Term [a]  =  60(1.2)ⁿ⁻² = 60(1.2)¹⁻² = 50

Common ratio [r]  =  1.2

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===========================

\sf Geometric \ Sum \ of  \ Terms = \dfrac{a(r^n - 1)}{r-1}

===========================

Solving Steps:

<em />\rightarrow \sf \dfrac{a(r^n - 1)}{r-1}<em />

<em />

<em />\rightarrow \sf \dfrac{50(1.2^{44} - 1)}{1.2-1}<em />

<em />

<em />\rightarrow \sf 761679.5808<em />

<em />

\rightarrow \sf 761680 \ \ \  (rounded \ to \ nearest \ integer)

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