Construct the Indicated Confidence Interval for the Difference Between the Two

question 93

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. $$\begin{array} { | c | c | } \hline \text { Type A } & \text { Type B } \\\hline \bar { x } _ { 1 } = 75.7 \mathrm { hrs } & \bar { x } _ { 2 } = 64.3 \mathrm { hrs } \\\hline s _ { 1 } = 4.5 \mathrm { hrs } & s _ { 2 } = 5.1 \mathrm { hrs } \\\hline n _ { 1 } = 11 & n _ { 2 } = 9 \\\hline\end{array}$$ Construct a $99 \%$ confidence interval for $\mu _ { 1 } - \mu _ { 2 }$ , the difference between the mean drying time for paint type A ar the mean drying time for paint type $B$ .

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

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Definitions:

Implicit Bias

Unconscious attitudes or stereotypes that affect an individual's understanding, actions, and decisions in an unconscious manner.

African-Americans

An ethnic group in the United States with ancestry tracing back to the black racial groups of Africa.

Killed

To cause the death of a living organism, often referred to in contexts ranging from biology to law and ethics.

Implicit Prejudice

Implicit prejudice refers to unconscious biases or attitudes individuals hold against others, which can influence behavior and decisions without conscious awareness.