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.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Chemistry Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

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

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Chemistry Textbooks

Inorganic Chemistry

Making Measurements

Chemical Reactions

Physical Chemistry

Chemistry Branches

The Earths Atmosphere

Study anywhere. Anytime. Across all devices.

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

Inorganic Chemistry

Making Measurements

Chemical Reactions

Physical Chemistry

Chemistry Branches

The Earths Atmosphere

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?