Step-by-step explanation:
Because we know the population standard deviation, we must use a Z-test.
Null hypothesis (H0): μ=50
Alternative hypothesis (H1): μ> 50
The decision rule is:
z-statistic< Z(z-student table (alpha/2)) --> You must accept the null hypothesis
z-statistic > Z (z-student table(alpha/2)) --> You must reject the null hypothesis
z-statistic formula:
z= (xbar-m)/(σ/(sqrt(n)))
xbar: sample mean
m: hypothesized value
σ: population standard deviation
n: number of observations
a)
z=(52.5-50)/(8/sqrt(60))
z= 2.42
The z-distribution table statistic at 2,5% (alpha/2) significance level is: 1.96 Because z-statistic is greater than the z-table value, we must reject the null hypothesis. It can be concluded that the population mean is greater than 50.
b)
z=(51-50)/(8/sqrt(60))
z= 0.96
The z-distribution table statistic at 2,5% (alpha/2)significance level is the same: 1.96 Because z-statistic is less than the z-table value, it cannot be concluded that the population mean is greater than 50.
c)
z=(51.8-50)/(8/sqrt(60))
z= 1.74
The z-distribution table statistic at 2,5%(alpha/2) significance level is the same: 1.96 Because z-statistic is less than the z-table value, it cannot be concluded that the population mean is greater than 50.
