Answer:
Step-by-step explanation:
Hello!
To get into context I'll define first the study variable.
X: Thickness of a polyethylene sheath.
The company won't purchase unless the standard deviation of sheath thickness is less than 0.06 mm, symbolically δ < 0.06
As a rule, the null hypothesis always states the "no change" case or the already known information about the study parameter, so it always carries the = symbol.
Note: Depending on the statistic course you are taking, you will be taught to do hypothesis tests for the standard deviation or that it is not valid to use it as a parameter. Personally, because δ is not directly a population parameter and, above all, because no statistic allows it to be studied directly. That is, to make a test for the standard deviation you have to use the Chi-square distribution, which includes the variance. I never use δ in the statistical hypotheses, just in case your course accept the hypothesis for the population standard deviation, here are the two options.
Hypotheses for δ
H₀: δ ≥ 0.06
H₁: δ < 0.06
Type I error:
Accept a shipment when it should have been rejected. (The standard deviation of sheath thickness is at least 0.06 mm)
Type II error:
Reject a shipment that should have been accepted. (The standard deviation of sheath thickness is less than 0.06 mm)
Hypotheses for δ₂
H₀: δ₂ ≥ 0.0036
H₁: δ₂ < 0.0036
Type I error:
Accept a shipment when it should have been rejected. (The population variance of sheath thickness is at least 0.0036 mm)
Type II error:
Reject a shipment that should have been accepted. (The population variance of sheath thickness is less than 0.0036 mm)
I hope it helps!
