Answer:
16 students
Step-by-step explanation:
144 students enter a spelling bee contest.
Step 1
For the semi final round we are told that only 1/6 of the group will make it into that round.
This is calculated as
1/6 × 144/students = 24 students.
This means that only 24 students would make it into the semi final rounds.
Step 2
We are also told in the question that only 2/3 of THAT group would make it into the final round.
" THAT" group been referred to in the question means the number students that made it to the semi final round
This is calculated as
2/3 of that group( the group that made it to the semi finals)
= 2/3 × 24 students
= 16 students.
Therefore, the number of students that will enter the final round of the spelling bee is 16 students.
Answer:
a) (iii) ANOVA
b) The ANOVA test is more powerful than the t test when we want to compare group of means.
Step-by-step explanation:
Previous concepts
Analysis of variance (ANOVA) "is used to analyze the differences among group means in a sample".
The sum of squares "is the sum of the square of variation, where variation is defined as the spread between each individual value and the grand mean"
If we assume that we have
groups and on each group from
we have
individuals on each group we can define the following formulas of variation:



And we have this property

Solution to the problem
Part a
(i) confidence interval
False since the confidence interval work just when we have just on parameter of interest, but for this case we have more than 1.
(ii) t-test
Can be a possibility but is not the best method since every time that we conduct a t-test we have a chance that we commit a Type I error.
(iii) ANOVA
This one is the best method when we want to compare more than 1 group of means.
(iv) Chi square
False for this case we don't want to analyze independence or goodness of fit, so this one is not the correct test.
Part b
The ANOVA test is more powerful than the t test when we want to compare group of means.
Answer:
I'm assuming that the cube is labelled 1-6. There are 6 * 6 * 6 = 216 total outcomes. There are 3 evens and 3 odds so there are 3 * 3 * 3 = 27 successful outcomes. Probability will be 27 / 216 = 1 / 8.
Answer:
The number of hits is 
Step-by-step explanation:
From the question we are told that
The ratio of the number of hits to the number of chances is equivalent to the batting average
The number of chances is j = 65 + 10 = 75
The number of hit so far is n = 25
Generally the batting average can be represented mathematically as

Here k is the number of additional hits Kyle need to get in order to obtain the batting average of 0.40 or more
So

=> 
Hence the number of hits for Kyle to get a batting average of 0.400 or greater by the end of the season is

=> 
=> 