Summer reading programs are very popular with children. At the Citizens Library,

Question

Summer reading programs are very popular with children. At the Citizens Library, Team Ramona read an average of 23.2 books with a standard deviation of 6.1. There were 21 members on this team. Team Beezus read an average of 26.1 books with a standard deviation of 2.3. There were 23 members on this team. Did the variances of the two teams differ?

Step 1: State hypothesis by filling in the symbol (=, <, >, or not equal):

Step 2: Find the critical value (from the table) (example 2.34)

Critical F value is:___________

Step 3: Compute the test value using the formula (round to two decimal places)

F test value is: ___________

Step 4: Reject the null or do not reject the null.

_______________

Step 5: Conclusion sentence ( is or is not)

There _____ enough evidence to support the claim that the variances of the two terms differ.

Explanation / Answer

Null Hypothesis, There Is No Significance between them Ho: ^2 = ^2
Alternate Hypothesis, There Is Significance between them H1: ^2 != ^2
Test Statistic
Sample 1
s1^2=37.21, n1 =21
Sample 2
s2^2 =5.29, n2 =23
Fo =37.21/5.29 = 7.03
| Fo | =7.03
Critical Value
The Value of |F | at LOS 0.05 with d.f F(n1-1,n2-1)=F(20,22) is 2.389
We got |Fo| =7.034 & | F | =2.389
Make Decision
Hence Value of | Fo | > | F | and Here we Reject Ho

ANS.
1.Ho: ^2 = ^2 ,H1: ^2 != ^2
2. F(n1-1,n2-1)=F(20,22) is 2.389
3. | Fo | =7.03
4. Reject Ho
5. There is enough evidence to support the claim that the variances of the two terms differ.

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