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Answer:
Part (A): The number of ways to select 12 jurors are 86493225.
Part (B): The number of ways to select 2 alternates are 306.
Part (C): Part (a) is an example of combination and Part (a) is an example of permutation
Step-by-step explanation:
Consider the provided information.
A band director wants to form a committee of 4 parents from a list of 45 band parents.
Part (A): How many different groups of 4 parents can the band director select?
Since order doesn't matter so we will use combination.
Use the formula for combination
Substitute n=45 and r=4 in above formula.
Hence, the number of ways are 148995.
Part (B) How many different ways can the band director select 4 parents to serve in the band parents’ association as president, vice president, treasurer, and secretary?
Since the order matter so we will use permutation:
The formula for permutation is:
Substitute n=45 and r=4 in above formula.
Hence, the number of ways are 3575880.
Part (C) . Explain the difference between parts (a) and (b) in terms of how you decided to solve each part.
Part (A) is an example of number of combination where order doesn't matter.
Part (B) is an example of permutation where order matter.
Answer:
Mean weight gained of two goods is not significantly different under 0.05 or 0.01 significance level, but it is under 0.10 significance level.
Step-by-step explanation:
We need to calculate the z-statistic of the differences of sample means and compare if it is significant under a significance level.
Z-score can be calculated using the formula:
z= where
- X is the mean weight gain for in the first three months after birth for babies using the Gibbs products.
- Y is the mean weight gain for in the first three months after birth for babies using the competitor products
- s(x) is the population standard deviation of the sample for Gibbs brand
- s(y) is the population standard deviation of the sample for competitor brand
- N(x) is the sample size for babies used Gibbs product
- N(y) is the sample size for babies used competitor product.
putting the numbers in the formula:
z= ≈ -1.51
and z-table gives that P(z<-1.51) = 0.0655
To conclude if the competitor good is significantly better, we need to choose a significance level and compare it to 0.0655.
For example, the difference in mean weight gained of two goods is not significant under 0.05 or 0.01 significance since 0.0655 is bigger than these values. But we can conclude that under 0.10 significance, competitor brand mean weight gain is significantly more than the Gibbs brand mean weight gain.