onsider the following hypothesis test: H 0: 50 H a: > 50 A sample of 50 is used and the population standard deviation is 6. Use the critical value approach to state your conclusion for each of the following sample results. Use = .05. a. With = 52.5, what is the value of the test statistic (to 2 decimals)? 2.42 Can it be concluded that the population mean is greater than 50? b. With = 51, what is the value of the test statistic (to 2 decimals)? 0.97 Can it be concluded that the population mean is greater than 50? c. With = 51.8, what is the value of the test statistic (to 2 decimals)? 1.74 Can it be concluded that the population mean is greater than 50?
Accepted Solution
A:
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 50c) 2.12 > 1.64 and we can conclude the same as in case aStep-by-step 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 51.8With value 52.5The test statistic z(e) ??a) z(e) = ( μ - μ₀ ) /( σ/√50) z(e) = (2.5*√50 )/6 z(e) = 2.942.94 > 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 50b) With value 51z(e) = ( μ - μ₀ ) /( σ/√50) ⇒ z(e) = √50/6 ⇒ z(e) = 1.18z(e) < z(c) we are in the acceptance region for H₀ we can conclude H₀ should be true. we can conclude population mean is 50c) the value 51.8z(e) = ( μ - μ₀ ) /( σ/√50) ⇒ z(e) = (1.8*√50)/ 6 ⇒ z(e) = 2.122.12 > 1.64 and we can conclude the same as in case a