Aaron wants to make as many gluten-free, low-carb cupcakes as he can for a bake sale. His recipe for 12 such cupcakes requires ⅜
2 answers:
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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
The slope of the given line is -4/5. The line perpendicular to that line will have a slope that is the opposite reciprocal. In other words, the perpendicular slope will be 5/4. If it passes through (4, 12), we have an x and a y value to use in y=mx+b. y is 12, x is 4, and we have a slope of 5/4. Filling in accordingly: 
and 12 = 5 + b. So b = 7. Rewriting with our new slope and b value, 
. And there you go!