Question

A sample of n = 16 individuals is randomly selected from a population with a mean...

A sample of n = 16 individuals is randomly selected from a population with a mean of μ = 65, and a treatment is administered to the individuals in the sample. After treatment, the sample mean is found to be M = 73.

(a) If the sample standard deviation is s = 11, are the data sufficient to conclude that the treatment has a significant effect using a two-tailed test with α = 0.05? (Round your answers to three decimal places.)

 t-critical = ± t =

(b) If the sample standard deviation is s = 18, are the data sufficient to conclude that the treatment has a significant effect using a two-tailed test with α = 0.05? (Round your answers to three decimal places.)

 t-critical = ± t =

df = n-1 = 16 - 1 = 15

a )

t critical = 2.131

t = M - / S / sqrt(n)

= 73 - 65 / 11 / sqrt(16)

= 2.909

Since test statistics falls in rejection region, Reject the null hypothesis

We conclude that we have sufficient evidence to support the claim.

b)

t critical = 2.131

t = M - / S / sqrt(n)

= 73 - 65 / 18 / sqrt(16)

= 1.778

Since test statistics falls in non-rejection region, Do not reject the null hypothesis

We conclude that we have insufficient evidence to support the claim.

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