Select Not independent or Independent for each situation.
2 answers:
Answer with explanation:
We know that if we select two items from a given set of items then the probability of selecting first item will effect the probability of selecting the second item.
Hence, the two events will be dependent.
But when the selection is done with replacement then the outcomes will be equal and hence, the probability of first event won't effect the probability of other.
Hence, the outcomes will be independent.
( Such a change happens because we know that the probability is defined as a number of favorable outcome to total number of outcomes and without replacement the total number of outcomes are different hence,one event get affected by the other)
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Answer:
1. The 99% confidence interval for the difference in average is -6.47377 < μ₁ - μ₂ < -11.34623
2. The possible issues in the calculations includes;
a. The confidence level used in the confidence interval can influence the result of the confidence interval observed
b. The sample size is small
Step-by-step explanation:
1. The number of adults with insomnia in the sample = 45
The number of adults that participated in the therapy, n₁ = 22
The number of candidates that served as control group, n₂ = 23
The average score for the for the 22 participants of the program, = 6.59
The standard deviation for the 22 participants of the program, s₁ = 4.10
The average score for the for the 23 subjects in the control group, = 15.50
The standard deviation for the 23 subjects in the control group, s₂ = 5.34
The confidence interval for unknown standard deviation, σ, is given by the following expression;
α = 1 - 0.99 = 0.01
α/2 = 0.005
The degrees of freedom, df = 22 - 1 = 21
=
= 1.721
Therefore, we have;
The 99% confidence interval for the difference in average is therefore given as follows;
-6.47377 < μ₁ - μ₂ < -11.34623
Therefore, there is considerable evidence that the participants in the survey had lower average score than the subjects in the control group
2. The possible issues in the calculations are;
a. The confidence level used in the confidence interval can influence the result of the confidence interval observed
b. The sample size is small