you want to make a confidence interval for the true average humidity at noon on uf campus in september. a random sample of 5 days reveals the following numbers: 55 62 63 63 76 what is the standard error of the sample mean, x-bar? important: keep all significant digits in your calculator until the very end.

The approximate standard deviation of a statistical sample population is known as the standard error (SE). By utilizing standard deviation, the standard error is a statistical concept that assesses how accurately a sample distribution represents a population.

The given humidities are 55 62 63 63 76

Do we have to find the standard error of the sample mean =?

The formula for the standard error is

SE = σ/n

The mean value is

x = (∑i[tex]x_{i}[/tex] )/n

= (55+62+63+63+76)/5

= 319/5

= 63.8

Now the standard deviation is

σ = √((∑i〖([tex]x_{i}[/tex] -μ)〗^2 )/(n-1))

= √(〖(53-63.8)〗^2+〖(62-63.8)〗^2+...........+〖(76-63.8)〗^2 )/(5-1)

= √((-116.64-3.24-0.64-0.64+148.84)/4)

= √(27.86/4)

= √6.92

= 2.630

The value of standard error is

SE = σ/√n

= 2.630/√5

= 2.630/2.230

= 1.1793

Therefore the standard error is 1.1793

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