Use calculator to evaluate each expression. (PICTURE) round to nearest hundredth.
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Answer:
Step-by-step explanation:
Hello!
The study variable is:
Xi: sugar level of a broth used to manufacture a pharmaceutical product (mg/mL) measured in day Di
Where i= 1, 2, 3
a) Using a significance level of 5% you need to test if the variability of the process on day 1 is greater than the variability of the process on day 2
The parameter that measures the variability of a given variable is the population variance δ², so in this item, you have to compare both population variances to test if the claim is correct. You have to do an F-ratio test, using the Snedecor-F distribution:
H₀: δ₁² ≤ δ₂²
H₁: δ₁² > δ₂²
α: 0.05
This test is one-tailed to the right this means that you will reject the null hypothesis to high values of the statistic:
The rejection region is F ≥ 2.69.
Using software I've calculated both sample variances:
Day 1: S₁²= 0.02
Day 2: S₂²= 0.15
Remember, this is an F-ratio test, under the null hypothesis we assume that δ₁²/δ₂²= 1 that is why I've replaced the variance ratio with 1.
b) The p-value for this test is:
P( ≥ 0.13)= 1 - P(
< 0.13) = 1 - 0.0006= 0.9994
The p-value is greater than α, the decision is to not reject the null hypothesis.
I hope this helps!