Question

In: Statistics and Probability

A pharmaceutical manufacturer purchases a particular material from two different suppliers. The mean level of impurities...

A pharmaceutical manufacturer purchases a particular material from two different suppliers. The mean level of impurities in the raw material is approximately the same for both suppliers, but the manufacturer is concerned about the variability of the impurities from shipment to shipment. To compare the variation in percentage impurities for the two suppliers, the manufacturer selects 9 shipments from each of the two suppliers and measures the percentage of impurities in the raw material for each shipment. The sample means and variances are shown in the table.

Supplier A	Supplier B
x₁ = 1.87	x₂ = 1.83
s₁² = 0.271	s₂² = 0.092
n₁ = 9	n₂ = 9

(a) Do the data provide sufficient evidence to indicate a difference in the variability of the shipment impurity levels for the two suppliers? Test using α = 0.01. Based on the results of your test, what recommendation would you make to the pharmaceutical manufacturer?

State the null and alternative hypotheses.

H₀: σ₁² = σ₂² versus H_a: σ₁² < σ₂²

H₀: σ₁² = σ₂² versus H_a: σ₁² ≠ σ₂²

H₀: σ₁² < σ₂² versus H_a: σ₁² > σ₂²

H₀: σ₁² ≠ σ₂² versus H_a: σ₁² = σ₂²

H₀: σ₁² = σ₂² versus H_a: σ₁² > σ₂²

State the test statistic. (Round your answer to two decimal places.)
F =

State the rejection region. (Round your answer to two decimal places.)
F >

State the conclusion.

H₀ is rejected. There is insufficient evidence to indicate that the supplier's shipments differ in variability.

H₀ is rejected. There is sufficient evidence to indicate that the supplier's shipments differ in variability.

H₀ is not rejected. There is sufficient evidence to indicate that the supplier's shipments differ in variability.

H₀ is not rejected. There is insufficient evidence to indicate that the supplier's shipments differ in variability.

(b) Find a 99% confidence interval for σ₂². (Round your answers to three decimal places.)

Interpret your results.

In repeated sampling, 1% of all intervals constructed in this manner will enclose σ₂².

There is a 1% chance that an individual sample variation will fall within the interval limits.

There is a 99% chance that an individual sample variation will fall within the interval.99% of all values will fall within the interval limits.

In repeated sampling, 99% of all intervals constructed in this manner will enclose σ₂².

Solutions

Expert Solution

The statistical software output for this problem is:

Hence,

a) Hypotheses: H₀: σ₁² = σ₂² versus H_a: σ₁² ≠ σ₂²

Test statistic = 2.95

Rejection region: F > 6.03

Conclusion: H₀ is not rejected. There is insufficient evidence to indicate that the supplier's shipments differ in variability.

b) 99% confidence interval:

(0.034, 0.548)

Interpretation: In repeated sampling, 99% of all intervals constructed in this manner will enclose σ₂².

orchestra answered 1 year ago

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