A researcher wishes to estimate the proportion of adults who have​ high-speed Internet access. What size sample should be obtained if she wishes the estimate to be within 0.03 with 95​% confidence if ​(a) she uses a previous estimate of 0.54​? ​(b) she does not use any prior​ estimates?

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A researcher wishes to estimate the proportion of adults who have​ high-speed Internet access. What size sample should be obtained if she wishes the estimate to be within
0.03
with
95​%
confidence if
​(a) she uses a previous estimate of
0.54​?
​(b) she does not use any prior​ estimates?
 
 
 

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Part 1
​(a)
n=enter your response here
​(Round up to the nearest​ integer.)
### Table of Critical Values

This table provides critical values for various confidence levels, which are important for statistical analysis, particularly in hypothesis testing.

#### Columns:
1. **Level of Confidence (1 - α): 100%**
   - Represents the confidence level for a statistical test.

2. **Area in Each Tail, α/2**
   - Indicates the probability of observing the test statistic in each tail of the distribution.

3. **Critical Value, Zᵦ**
   - The cutoff value that defines the regions where the null hypothesis is either rejected or not rejected.

#### Data:
- **99% Confidence Level**:
  - Area in Each Tail: 0.005
  - Critical Value: 2.575

- **95% Confidence Level**:
  - Area in Each Tail: 0.025
  - Critical Value: 1.96

- **90% Confidence Level**:
  - Area in Each Tail: 0.05
  - Critical Value: 1.645

These critical values are used to determine the threshold for significance in hypothesis testing. For example, in a 95% confidence level test, the critical value is 1.96, meaning you would reject the null hypothesis if your test statistic exceeds this value.
Transcribed Image Text:### Table of Critical Values This table provides critical values for various confidence levels, which are important for statistical analysis, particularly in hypothesis testing. #### Columns: 1. **Level of Confidence (1 - α): 100%** - Represents the confidence level for a statistical test. 2. **Area in Each Tail, α/2** - Indicates the probability of observing the test statistic in each tail of the distribution. 3. **Critical Value, Zᵦ** - The cutoff value that defines the regions where the null hypothesis is either rejected or not rejected. #### Data: - **99% Confidence Level**: - Area in Each Tail: 0.005 - Critical Value: 2.575 - **95% Confidence Level**: - Area in Each Tail: 0.025 - Critical Value: 1.96 - **90% Confidence Level**: - Area in Each Tail: 0.05 - Critical Value: 1.645 These critical values are used to determine the threshold for significance in hypothesis testing. For example, in a 95% confidence level test, the critical value is 1.96, meaning you would reject the null hypothesis if your test statistic exceeds this value.
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