Question

a A random sample of eight observations was taken from a normal population. The sample mean and standard deviation are x = 75 and s = 50. Can we infer at the 10% significance level that the population mean is less than 100?

b Repeat part (a) assuming that you know that the population standard deviation is σ = 50.

c Review parts (a) and (b). Explain why the test statistics differed.

Answer 1

Answer:

a)

Given,

Ho : u = 100

Ho : u < 100

test statistic t = (x - u)/(s/sqrt(n))

substitute values

= (75 - 100)/(50/sqrt(8))

= - 1.41

degree of freedom = n - 1 = 8 - 1 = 7

P value = 0.100695

= 0.1007

Here we observe that, p value > alpha, so we fail to reject Ho.

So there is no sufficient evidence to support the claim.

b)

Ho : u = 100

Ha : u < 100

test statistic z = (x - u)/(s/sqrt(n))

substitute values

= (75 - 100)/(50/sqrt(8))

= - 1.41

P value = 0.0792698 [since from z table]

= 0.0793

Here we observe that, p value < alpha, so we reject Ho.

So there is sufficient evidence to support the claim.

c)

Based on a & b we can say that, conclusion part of both are different.