You entered a number set of (1,2,3,4,5).
Use the sign test for a sample size to test the null hypothesis μ = 2 against the alternative hypothesis H1: μ < 2 at the 0.02 level of significance:
From those 1 numbers you entered, 1 of them are not equal to our H0: μ = 2. We denote this count as n. 0 of those 1 numbers are > 2, denoted as x. 1 of the numbers are < 2
For a large sample size, we use the normal approximation to the binomial distribution where θ = 0.5
First, we pick up our z-score value based on our significance level 0.02 which is -2.05. This will be our benchmark to compare to.
Calculate Mean (μ)
μ = nθ
μ = 1(0.5)
μ = 0.5
Calculate Variance (σ)
σ = √nθ(1 - θ)
σ = √(1)(0.5)(1 - 0.5)
σ = √1(0.25)
σ = √0.25
σ = 0.5
Now calculate our Z-score (Z)
| Z = | x - μ | |
| σ |
| Z = | 0 - 0.5 | |
| 0.5 |
| Z = | -0.5 | |
| 0.5 |
Z = -1
