Chapter 0: Q4-4 TY (page 1)

If there had been $n = 13$ replications in both data sets, would the difference in standard deviations be significant?

Short Answer

Expert verified

Here, $F_{calculated} = 2.82 > F_{table} = 2.69 .$ .

Hence, the differences in the standard deviation of the two given sets are significant.

Step by step solution

F test

F-test: $F_{calculated} = \frac{{S_{1}}^{2}}{{Z_{2}}^{2}}$

Using F-test

The number of replications in both data sets,

Using Table 4-2, we know that,

F-Test:

On considering larger a larger standard deviation in the numerator, we. We have:,

$s_{1} = 0.47 s_{1} = 0.28$

Using F-test, the

F

is calculated as follows:,

role="math" localid="1663326924581" $F_{calculated} = \frac{{s_{1}}^{2}}{{s^{2}}_{1}} = \frac{{(0.47)}^{2}}{{(0.28)}^{2}} = 2.82 .$

Degree of Freedom for Both

The degrees of freedom for $s_{1}$ are $(n - 1 \Rightarrow 13 - 1 = 12) .$

From Table 4-3, by locating, the column with 12 degrees of freedom for role="math" localid="1663326886623" $s_{1}$ and the row with 12 degrees of freedom for $s_{2}$ give.

Compare $F_{calculated}$ with $F_{table}$ .

$F_{calculated} = 2.82 > F_{table} = 2.69 .$

Therefore, the differences in the standard deviation of the two given sets are significant.

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If there had been $n = 13$ replications in both data sets, would the difference in standard deviations be significant?

Short Answer

Step by step solution

F test

Using F-test

Degree of Freedom for Both

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If there had beenn=13replications in both data sets, would the difference in standard deviations be significant?

Short Answer

Step by step solution

F test

Using F-test

Degree of Freedom for Both

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Chemistry Textbooks

Making Measurements

Chemistry Branches

Ionic and Molecular Compounds

Nuclear Chemistry

Organic Chemistry

Physical Chemistry

Study anywhere. Anytime. Across all devices.

If there had been $n = 13$ replications in both data sets, would the difference in standard deviations be significant?