Test and CI for One Proportion Sample X N Sample p ___% Lower Bound 1 34 50 0.68
ID: 3301071 • Letter: T
Question
Test and CI for One Proportion
Sample X N Sample p ___% Lower Bound
1 34 50 0.680000 0.555377
Test and CI for One Proportion
Sample X N Sample p ___% Lower Bound
1 34 50 0.680000 0.581029
We are operating a highly profitable catfish farm. To assess the proportion of our fish that are over 9.5 lbs., we randomly sample 50 and get 34 heavier than 9.5 lbs. Above, we have used the Exact method to compute both the 90% and 95% Lower Bounds.
Which of the above is the 95% Lower Bound?
Give a correct interpretation of the 95% Lower Bound.
Use Minitab to compute with the Exact method the 99% Lower Bound based on this sample. Briefly explain why it is lower than the 95% Lower Bound.
Explanation / Answer
Answer:
Test and CI for One Proportion
Method
p: event proportion
Exact method is used for this analysis.
Descriptive Statistics
N
Event
Sample p
95% Lower Bound
for p
50
34
0.680000
0.555377
p: event proportion
Exact method is used for this analysis.
Descriptive Statistics
N
Event
Sample p
90% Lower Bound
for p
50
34
0.680000
0.581029
95% lower bound is 0.555377
We are 95% confident that real proportion falls above the lower bound 0.555377.
Descriptive Statistics
N
Event
Sample p
99% Lower Bound
for p
50
34
0.680000
0.506948
99% lower bound is lower than the 95% Lower Bound because we use more confidence of containing true proportion. The z value used to calculate 95% lower bound is -1.645 and 99% lower bound is -2.326. As the level of confidence increases, lowerbound decreases.
p: event proportion
Exact method is used for this analysis.
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