During the 2016 season, Lauren Robinson had 92 at bats and made 36 hits. Calculate a 95%
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.
![**Example Problem:**
During the 2016 season, Lauren Robinson had 92 at bats and made 36 hits. Calculate a 95% confidence interval for her **ability** to get hits in that season.
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**To solve this problem, follow these steps:**
1. **Calculate the sample proportion of hits:**
\[ \hat{p} = \frac{\text{Number of hits}}{\text{Number of at bats}} \]
\[ \hat{p} = \frac{36}{92} \]
\[ \hat{p} \approx 0.3913 \]
2. **Determine the standard error (SE) of the proportion:**
\[ SE = \sqrt{\frac{\hat{p} (1 - \hat{p})}{n}} \]
\[ SE = \sqrt{\frac{0.3913 \times (1 - 0.3913)}{92}} \]
\[ SE \approx 0.0507 \]
3. **Find the critical value (z*) for a 95% confidence interval:**
(For a 95% confidence level, the critical value z* is approximately 1.96.)
4. **Calculate the margin of error (ME):**
\[ ME = z^* \times SE \]
\[ ME = 1.96 \times 0.0507 \]
\[ ME \approx 0.0994 \]
5. **Calculate the confidence interval:**
\[ \text{Confidence Interval} = \hat{p} \pm ME \]
\[ \text{Confidence Interval} \approx 0.3913 \pm 0.0994 \]
Thus, the interval is:
\[ \text{Confidence Interval} \approx (0.2919, 0.4907) \]
**Conclusion:**
With 95% confidence, we can say that Lauren Robinson's ability to get hits during the 2016 season is between approximately 29.19% and 49.07%.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc4e58655-e53f-42ee-b39f-787912eba8a6%2Ffbf6581b-1aa0-47b0-beb6-0b210db721f1%2Fvo6wnrg_processed.png&w=3840&q=75)
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