The Sample Standard Deviations and Sample Sizes Are Given for Independent

question 22

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.
- $\mathrm { s } _ { 1 } = 32.2 , \mathrm { n } _ { 1 } = 61 , \mathrm {~s} _ { 2 } = 26.8 , \mathrm { n } _ { 2 } = 31 \text {; right-tailed test, } \alpha = 0.01$

• A)Test statistic: \(\mathrm { F } = 38.69\). Critical value \(= 2.03\). Reject \(\mathrm { H } _ { 0 }\).
• B) Test statistic: \(\mathrm { F } = 1.44\). Critical value \(= 2.21\). Do not reject \(\mathrm { H } _ { 0 }\).
• C) Test statistic: \(\mathrm { F } = 1.44\). Critical value \(= 2.03\). Reject \(\mathrm { H } _ { 0 }\).
• D) Test statistic: \(\mathrm { F } = 1.2\). Critical value \(= 2.21\). Do not reject \(\mathrm { H } _ { 0 }\).

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Definitions:

Null Hypothesis

A default statement that there is no effect or no difference, used as a starting point for statistical hypothesis testing.

Degrees of Freedom

The number of independent values or quantities which can be assigned to a statistical distribution.

Chi-square Statistic

A statistical measure used to determine if there is a significant difference between the expected frequencies and the observed frequencies in one or more categories.

Wearing Glasses

The act of using corrective lenses mounted in frames that rest on the face to improve vision or protect the eyes.