Question

In: Statistics and Probability

Assuming the population has an approximate normal distribution, if a sample size n = 24 has...

Assuming the population has an approximate normal distribution, if a sample size n = 24 has a sample mean ¯ x = 49 with a sample standard deviation s = 2 , find the margin of error at a 99% confidence level. THEN YOU MUST ROUND TO TWO DECIMALS..

Expert Solution

Solution :

Given that,

Point estimate = sample mean = = 49

sample standard deviation = s = 2

sample size = n = 24

Degrees of freedom = df = n - 1 = 24 - 1 = 23

At 99% confidence level the t is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

t /2,df = t0.005,23 = 2.807

Margin of error = E = t/2,df * (s / $\sqrt$ n)

= 2.807 * (2 / $\sqrt$ 24)

Margin of error = E = 1.15

orchestra answered 2 years ago

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