Construct the Indicated Confidence Interval for the Difference Between the Two

question 31

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. Also assume that the population standard deviations are equal $\left( \sigma _ { 1 } = \sigma _ { 2 } \right)$ , so that the standard error of the difference between means is obtained by pooling the sample variances. A paint manufacturer wanted 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 99 % confidence interval for $\mu _ { 1 } - \mu _ { 2 }$ the difference between the mean drying time for paint type A and the mean drying time for paint type B.

• A) \(- 1.51 \mathrm { hrs } < \mu _ { 1 } - \mu _ { 2 } < 7.51 \mathrm { hrs }\)
• B) \(- 2.24 \mathrm { hrs } < \mu _ { 1 } - \mu _ { 2 } < 8.24 \mathrm { hrs }\)
• C) \(- 1.00 \mathrm { hrs } < \mu _ { 1 } - \mu _ { 2 } < 7.00 \mathrm { hrs }\)
• D) \(- 0.14 \mathrm { hrs } < \mu _ { 1 } - \mu _ { 2 } < 6.14 \mathrm { hrs }\)

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Definitions:

Null Hypothesis

A statement in inferential statistics that there is no effect or no difference, and any observed deviation from this state is due to chance.

Rejection Level

The threshold or critical value that determines whether to reject the null hypothesis in statistical hypothesis testing, often denoted by alpha.

P-value

A measure in statistical hypothesis testing that quantifies the evidence against a null hypothesis, with lower values indicating stronger evidence.

Sample Mean

The average of a set of observations or values taken from a sample of a population.