The Sample Standard Deviations and Sample Sizes Are Given for Independent

question 80

Multiple Choice

The sample standard deviations and sample sizes are given for independent simple random samples from twopopulations. Use the two-standard-deviations F-test to conduct the required hypothesis test.
- $\mathrm { s } _ { 1 } = 0.0782 , \mathrm { n } _ { 1 } = 9$ , $\mathrm { s } _ { 2 } = 0.2300 , \mathrm { n } _ { 2 } = 10$ ; left-tailed test, $\alpha = 0.05$

• A)Test statistic: \(\mathrm { F } = 0.116\) Critical value: \(0.318\). Do not reject \(\mathrm { H } _ { 0 }\).
• B) Test statistic: \(\mathrm { F } = 0.116\) Critical value: \(0.310\). Reject \(\mathrm { H } _ { 0 }\).
• C) Test statistic: \(F = 0.116\) Critical value: \(0.295\). Do not reject \(\mathrm { H } _ { 0 }\).
• D) Test statistic: \(F = 0.116\) Critical value: \(0.295\). Reject \(\mathrm { H } _ { 0 }\).

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Definitions:

Defects

Imperfections or faults in a product or process that deviate from desired performance or specification.

Normal Distribution

This denotes a probability distribution with symmetry at the mean, proving that nearer-to-mean data points occur more regularly than those farther away.

Mean

The mean of a collection of numbers, found by dividing their total sum by the quantity of numbers in the set.

μ

The symbol commonly used to represent the mean or average of a population in statistics.