Answer:
a) z(e) > z(c) 2.94 > 1.64 we are in the rejection zone for H₀ we can conclude sample mean is great than 50. We don´t know how big is the population .We can not conclude population mean is greater than 50
b) z(e) < z(c) 1.18 < 1.64 we are in the acceptance region for H₀ we can conclude H₀ should be true. we can conclude population mean is 50
c) 2.12 > 1.64 and we can conclude the same as in case a
Explanation:
The problem is concerning test hypothesis on one tail (the right one)
The critical point z(c) ; α = 0.05 fom z table w get z(c) = 1.64 we need to compare values (between z(c) and z(e) )
The test hypothesis is:
a) H₀ ⇒ μ₀ = 50 a) Hₐ μ > 50 ; for value 52.5
b) Hₐ μ > 50 ; for value 51
c) Hₐ μ > 50 ; for value 51.8
With value 52.5
The test statistic z(e) ??
a) z(e) = ( μ - μ₀ ) /( σ/√50) z(e) = (2.5*√50 )/6 z(e) = 2.94
2.94 > 1.64 we are in the rejected zone for H₀ we can conclude sample mean is great than 50. We don´t know how big is the population .We can not conclude population mean is greater than 50
b) With value 51
z(e) = ( μ - μ₀ ) /( σ/√50) ⇒ z(e) = √50/6 ⇒ z(e) = 1.18
z(e) < z(c) we are in the acceptance region for H₀ we can conclude H₀ should be true. we can conclude population mean is 50
c) the value 51.8
z(e) = ( μ - μ₀ ) /( σ/√50) ⇒ z(e) = (1.8*√50)/ 6 ⇒ z(e) = 2.12
2.12 > 1.64 and we can conclude the same as in case a