According to a newspaper, 78% of high school seniors have a driver's license. Suppose we take a random sample of 200 high proportion who have a driver's license. a. What value should we expect for our sample proportion? b. What is the standard error? c. Use your answers to parts (a) and (b) to complete this sentence: We expect d. Suppose we increased the sample size from 200 to 800. What effect would this have on the standard error? Recalculate the prediction was correct. % to have their driver's license, give or take %. a. We should expect a sample proportion of %. (Type an integer or a decimal. Do not round.) b. The standard error is. (Type an integer or decimal rounded to three decimal places as needed.) c. Use your answers to fill in the blanks below. We expect % of students to have a driver's license, give or take %. (Type integers or decimals rounded to one decimal place as needed.) d. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or decimal rounded to one decimal place as needed.) %. O A. The standard error would decrease. The new standard error is laulatio Ofter nerforming the

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**Problem: Estimating Sample Proportions of High School Seniors with Driver's Licenses**

According to a newspaper, 78% of high school seniors have a driver's license. Suppose we take a random sample of 200 high school seniors and find the proportion who have a driver's license.

1. **What value should we expect for our sample proportion?**
2. **What is the standard error?**
3. **Use your answers to parts (a) and (b) to complete this sentence:**
   We expect _____% to have their driver's license, give or take ______%.

4. **Suppose we increased the sample size from 200 to 800. What effect would this have on the standard error? Recalculate the standard error to see if your prediction was correct.**

---

**a. We should expect a sample proportion of ____%.
(Type an integer or a decimal. Do not round.)**

**b. The standard error is ____%.**
(Type an integer or decimal rounded to three decimal places as needed.)

**c. Use your answers to fill in the blanks below:**

   We expect _____% of students to have a driver's license, give or take ______%.
   (Type integers or decimals rounded to one decimal place as needed.)

**d. Select the correct choice below and fill in the answer box to complete your choice.**

   (Type an integer or decimal rounded to one decimal place as needed.)

- ○ A. The standard error would decrease. The new standard error is __________%.
- ○ B. We cannot determine what would happen to the standard error without performing the calculation. After performing the calculation, the new standard error is __________%.
- ○ C. The standard error would increase. The new standard error is __________%.
- ○ D. The standard error would remain the same. The standard error is still __________%.

---

*Note: Please perform the necessary calculations to find expected values and standard errors.*
Transcribed Image Text:**Problem: Estimating Sample Proportions of High School Seniors with Driver's Licenses** According to a newspaper, 78% of high school seniors have a driver's license. Suppose we take a random sample of 200 high school seniors and find the proportion who have a driver's license. 1. **What value should we expect for our sample proportion?** 2. **What is the standard error?** 3. **Use your answers to parts (a) and (b) to complete this sentence:** We expect _____% to have their driver's license, give or take ______%. 4. **Suppose we increased the sample size from 200 to 800. What effect would this have on the standard error? Recalculate the standard error to see if your prediction was correct.** --- **a. We should expect a sample proportion of ____%. (Type an integer or a decimal. Do not round.)** **b. The standard error is ____%.** (Type an integer or decimal rounded to three decimal places as needed.) **c. Use your answers to fill in the blanks below:** We expect _____% of students to have a driver's license, give or take ______%. (Type integers or decimals rounded to one decimal place as needed.) **d. Select the correct choice below and fill in the answer box to complete your choice.** (Type an integer or decimal rounded to one decimal place as needed.) - ○ A. The standard error would decrease. The new standard error is __________%. - ○ B. We cannot determine what would happen to the standard error without performing the calculation. After performing the calculation, the new standard error is __________%. - ○ C. The standard error would increase. The new standard error is __________%. - ○ D. The standard error would remain the same. The standard error is still __________%. --- *Note: Please perform the necessary calculations to find expected values and standard errors.*
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