Construct the Indicated Confidence Interval for the Difference Between the Two

question 48

Multiple Choice

Construct the indicated confidence interval for the difference between the two population means. Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. A paint manufacturer wished to compare the drying times of two different types of paint. Independent simple random samples of 11 cans of type A and 9 cans of type B were selected and applied to similar surfaces. The drying times, in hours, were recorded. The summary statistics are as follows.

Construct a 98% confidence interval for $\mu _ { 1 } - \mu _ { 2 }$ the difference between the mean drying time for paint of type A and the mean drying time for paint of type B.

• A) \(6.08 \mathrm { hrs } < \mu _ { 1 } - \mu _ { 2 } < 16.72 \mathrm { hrs }\)
• B) \(5.92 \mathrm { hrs } < \mu _ { 1 } - \mu _ { 2 } < 16.88 \mathrm { hrs }\)
• C) \(5.85 \mathrm { hrs } < \mu _ { 1 } - \mu _ { 2 } < 16.95 \mathrm { hrs }\)
• D) \(5.78 \mathrm { hrs } < \mu _ { 1 } - \mu _ { 2 } < 17.02 \mathrm { hrs }\)

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Definitions:

Quick Ratio

A financial metric that measures a company's ability to cover its short-term liabilities with its most liquid assets, excluding inventory.

Current Liabilities

Short-term financial obligations due within one year or within the entity's operating cycle if longer.

Debt-Paying Ability

An indication of a company's financial strength, referring to its capacity to meet its debt obligations as they come due.

Solvency

The ability of a company or individual to meet long-term financial obligations, indicating financial health.