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Confldence intervals and Hypothesis Testing
Danlette
Computing and comparing confidence intervals for a population...
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You are looking at a population and are interested in the proportion that has a certaln characteristic. Unknown to you, this population proportion is .
You have taken a random sample of size from the population and found that the proportion of the sample that has the characteristic is . Your sample is Sample 1 in the table below. (In the table, Sample 1 is written "S1", Sample 2 is written "S2", etc.)
(a) Based on Sample 1, graph the and confidence intervals for the population proportion. Use 1.150 for the critical value for the confidence interval, and use 1.645 for the critical value for the confidence interval. (If necessary, consult a list of formulas.)
- Enter the lower and upper limits on the graphs to show each confidence interval. Write your answers with two decimal places.
- For the points ( and ), enter the population proportion, 0.85 .
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(4)
(b) Press the "Generate Samples" button below to simulate taking 19 more samples of size from the same population. Notice that the confidence intervals for these samoles are drawn automaticallv, Then complete parts (c) and ( ) below the table.
Explanation
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Studdy Solution
STEP 1
1. The true population proportion is .
2. The sample proportion is .
3. The sample size is .
4. We are using the normal approximation to construct confidence intervals.
STEP 2
1. Calculate the standard error of the sample proportion.
2. Compute the 75% confidence interval.
3. Compute the 90% confidence interval.
STEP 3
Calculate the standard error (SE) of the sample proportion using the formula:
Substitute the given values:
STEP 4
Compute the 75% confidence interval using the critical value 1.150:
Lower limit:
Upper limit:
The 75% confidence interval is .
STEP 5
Compute the 90% confidence interval using the critical value 1.645:
Lower limit:
Upper limit:
The 90% confidence interval is .
The confidence intervals are:
- 75% confidence interval:
- 90% confidence interval:
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