Round your answers to two decimal places. A. With 90% confidence the proportion of all people who will buy a cell phone this year is between and B. If many groups of 800 randomly selected people were surveyed, then a different confidenc interval would be produced from each group. About percent of these confidence intervals will contain the true population proportion of people who will buy a new cell phone this year and about percent will not contain the true populati proportion.
Round your answers to two decimal places. A. With 90% confidence the proportion of all people who will buy a cell phone this year is between and B. If many groups of 800 randomly selected people were surveyed, then a different confidenc interval would be produced from each group. About percent of these confidence intervals will contain the true population proportion of people who will buy a new cell phone this year and about percent will not contain the true populati proportion.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Problem 1P
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![### Calculating a 90% Confidence Interval for Proportion of New Cell Phone Buyers
You're interested in constructing a 90% confidence interval for the proportion of people who will buy a new cell phone this year. Out of the 800 randomly selected people surveyed, 382 are expected to buy a new cell phone this year.
Round your answers to two decimal places.
#### A. Confidence Interval Calculation
With 90% confidence, the proportion of all people who will buy a cell phone this year is estimated to be between:
- [ ]
and
- [ ].
#### B. Interpretation of Confidence Interval
If many groups of 800 randomly selected people were surveyed, then a different confidence interval would be produced from each group. About:
- [ ] %
of these confidence intervals will contain the true population proportion of people who will buy a new cell phone this year, and about:
- [ ] %
will not contain the true population proportion.
To calculate the confidence interval, follow these steps:
1. **Calculate the sample proportion (p̂):**
\[
p̂ = \frac{382}{800}
\]
2. **Find the standard error (SE) of the proportion:**
\[
SE = \sqrt{\frac{p̂(1 - p̂)}{n}}
\]
3. **Determine the Z-value for a 90% confidence interval (Z₀.₀₅):**
For a 90% confidence level, Z-value ≈ 1.645 (from Z-tables).
4. **Calculate the margin of error (ME):**
\[
ME = Z₀.₀₅ \times SE
\]
5. **Construct the confidence interval:**
- Lower Boundary = \( p̂ - ME \)
- Upper Boundary = \( p̂ + ME \)
Insert these values into the provided blanks to complete the interval estimation. This process ensures that with 90% confidence, the specified range accurately encompasses the true proportion of potential new cell phone buyers in the population.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd1a73d04-4829-40e4-8e78-0a30aa84e71e%2F4b1b4afa-1b51-4650-9eac-66c85b30e224%2Fvcu8slc_processed.png&w=3840&q=75)
Transcribed Image Text:### Calculating a 90% Confidence Interval for Proportion of New Cell Phone Buyers
You're interested in constructing a 90% confidence interval for the proportion of people who will buy a new cell phone this year. Out of the 800 randomly selected people surveyed, 382 are expected to buy a new cell phone this year.
Round your answers to two decimal places.
#### A. Confidence Interval Calculation
With 90% confidence, the proportion of all people who will buy a cell phone this year is estimated to be between:
- [ ]
and
- [ ].
#### B. Interpretation of Confidence Interval
If many groups of 800 randomly selected people were surveyed, then a different confidence interval would be produced from each group. About:
- [ ] %
of these confidence intervals will contain the true population proportion of people who will buy a new cell phone this year, and about:
- [ ] %
will not contain the true population proportion.
To calculate the confidence interval, follow these steps:
1. **Calculate the sample proportion (p̂):**
\[
p̂ = \frac{382}{800}
\]
2. **Find the standard error (SE) of the proportion:**
\[
SE = \sqrt{\frac{p̂(1 - p̂)}{n}}
\]
3. **Determine the Z-value for a 90% confidence interval (Z₀.₀₅):**
For a 90% confidence level, Z-value ≈ 1.645 (from Z-tables).
4. **Calculate the margin of error (ME):**
\[
ME = Z₀.₀₅ \times SE
\]
5. **Construct the confidence interval:**
- Lower Boundary = \( p̂ - ME \)
- Upper Boundary = \( p̂ + ME \)
Insert these values into the provided blanks to complete the interval estimation. This process ensures that with 90% confidence, the specified range accurately encompasses the true proportion of potential new cell phone buyers in the population.
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