A software developer wants to know how many new computer games people buy each year. A sample of 1064 people was taken to study their purchasing habits. Construct the 99% confidence interval for the mean number of computer games purchased each year if the sample mean was found to be 9.6. Assume that the population standard deviation is 1.8. Round your answers to one decimal place.
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
![### Confidence Interval Calculation Example
#### Problem Statement:
A software developer wants to know how many new computer games people buy each year. A sample of 1064 people was taken to study their purchasing habits. Construct the 99% confidence interval for the mean number of computer games purchased each year if the sample mean was found to be 9.6. Assume that the population standard deviation is 1.8. Round your answers to one decimal place.
#### Solution:
To calculate the 99% confidence interval for the mean, use the following formula:
\[ CI = \bar{x} \pm Z \left(\frac{\sigma}{\sqrt{n}}\right) \]
Where:
- \(\bar{x}\) = Sample mean = 9.6
- \(Z\) = Z-value for 99% confidence (approx. 2.576)
- \(\sigma\) = Population standard deviation = 1.8
- \(n\) = Sample size = 1064
**Steps:**
1. Calculate the standard error (SE) of the mean:
\[ SE = \frac{\sigma}{\sqrt{n}} = \frac{1.8}{\sqrt{1064}} \]
2. Multiply the standard error by the Z-value to find the margin of error (MOE):
\[ MOE = Z \times SE \]
3. Calculate the confidence interval:
- Lower endpoint: \(\bar{x} - MOE\)
- Upper endpoint: \(\bar{x} + MOE\)
Insert the calculated values into the answer boxes.
#### Answer Section:
- **Lower endpoint:** [Input calculated value]
- **Upper endpoint:** [Input calculated value]
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### Note:
Use the "Tutor" feature if you need assistance with understanding the concepts or calculations. Always ensure answers are rounded to one decimal place as specified.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F07e0be5e-c198-4d18-a515-6f255afa67b7%2F37169778-6cf4-4455-9e2f-764f42d5f809%2Fy8tiqtk_processed.jpeg&w=3840&q=75)
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