How do you find a critical value when using a 1% significance level

[laura_a]

Homework Statement

The data I'm working with is
Sample mean(voltage)=128.25
variance=9/20
sample size=20
SD=3
Z=-2.61

The Attempt at a Solution

The first part of what I was doing was a hypothesis test that the true voltage is 130 compared to the alternative less than 130. Which I worked out the Z= -2.61

What I have to do now is calculate the critical value for this test using a 1% significance level.. I know the answer because I looked it up in the textbook its 128.44 but for the life of me I can't work out any formulas that will help me... can anyone shed some light? Thanks :)

 

[lippyka]

The critical value for this test is 128.44. That's the value that determines whether the hypothesis can be rejected or not. To calculate the critical value, you need to use the z-score formula: z = (x - μ)/σ, where x is the sample mean (128.25), μ is the population mean (130) and σ is the standard deviation (3). Plugging in the values gives you a z-score of -2.61, which is the critical value.