7.
Determine whether it is appropriate to apply the Central Limit Theorem for Proportions: sample size 35, sample proportion 0.95.
A)
Yes
B)
No
yes
Yes
No
To determine whether it is appropriate to apply the Central Limit Theorem for Proportions, we need to consider the conditions required for its application.
The Central Limit Theorem states that for a large enough sample size, the sampling distribution of the sample proportion will be approximately normal, regardless of the shape of the population distribution, as long as certain conditions are met.
The conditions for applying the Central Limit Theorem for Proportions are:
1) Random Sampling: The data should be obtained through a random sampling method to ensure that the sample is representative of the population.
2) Independence: Each observation in the sample must be independent of each other. This means that the observations should not be influenced by each other.
3) Success/Failure Condition: This condition requires that both np and n(1-p) be greater than or equal to 10, where n is the sample size and p is the sample proportion.
In this case, the sample size is 35 and the sample proportion is 0.95. To check the success/failure condition, we can calculate np and n(1-p):
np = 35 * 0.95 = 33.25
n(1-p) = 35 * (1 - 0.95) = 1.75
Both np and n(1-p) are greater than 10, so the success/failure condition is satisfied.
Therefore, it is appropriate to apply the Central Limit Theorem for Proportions in this case. So, the answer is A) Yes.