A random selection of volunteers at a research institute has been exposed to a weak flu virus. After the volunteers began to have flu symptoms, 20 of them were given multivitamin tablets daily that contained 1 gram of vitamin C and 3 grams of various other vitamins and minerals. The remaining 20 volunteers were given tablets containing 4 grams of vitamin C only. For each individual, the length of time taken to recover from the flu was recorded. At the end of the experiment the following data were obtained. Days to recover from flu Treated with 8.5, 5.6, 8.8. 6.1. 6.1, 3.3. 8.9, 6.0, 3.3, 9.7, 6.0. 9.3, 2.3. 4.6. 5.5.6.7. 6.6. 4.9. 10.0.6.6 multivitamin Treated with 6.5, 5.0, 3.2, 4.7, 3.5, 2.7, 3.8, 4.4, 4.6, 3.6, 4.0, 2.7, 3.2, 4.8, 6.3, 7.5, 6.9, 4.7, 4.8, 1.3 vitamin C Send data to calculator ✓ Send data to Excel Suppose that it is known that the population standard deviation of recovery time from the flu is 1.8 days when treated with multivitamins and that the population standard deviation of recovery time from the flu is 1.5 days when treated with vitamin C tablets. Suppose also that both populations are approximately normally distributed. Construct a 90% confidence interval for the difference ₁-₂ between the mean recovery time when treated with multivitamins (μ₁) and the mean recovery time when treated with vitamin C only (₂). Then find the lower limit and upper limit of the 90% confidence interval. Carry your intermediate computations to at least three decimal places. Round your answers to at least two decimal places. (If necessary, consult a list of formulas.) Lower limit: Upper limit: X

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**Study on Recovery Time from Flu**

A research study investigated the effects of multivitamins and vitamin C on recovery time from a flu virus. Participants were split into two groups, each receiving different treatments and recovery times were measured. The study concluded with the following results:

**Data Collected:**
- **Treated with Multivitamin:** Recovery times in days: 8.5, 5.6, 8.8, 6.1, 6.1, 3.3, 8.9, 6.0, 3.3, 9.7, 6.0, 9.3, 2.3, 4.6, 5.5, 6.7, 6.6, 4.9, 10.0, 6.6
- **Treated with Vitamin C:** Recovery times in days: 6.5, 5.0, 3.2, 4.7, 3.5, 2.7, 3.8, 4.4, 4.6, 3.6, 4.0, 2.7, 3.2, 4.8, 6.3, 7.5, 6.9, 4.7, 4.8, 1.3

**Objective:**
Calculate a 90% confidence interval for the difference in mean recovery times between the two groups: those treated with multivitamins (\( \mu_1 \)) and those treated with vitamin C only (\( \mu_2 \)).

**Known Population Parameters:**
- Standard deviation of recovery with multivitamins: 1.8 days
- Standard deviation of recovery with vitamin C: 1.5 days

**Instructions for Calculation:**
1. Use the collected data to compute the mean recovery times for both groups.
2. Calculate the 90% confidence interval for the difference in means (\( \mu_1 - \mu_2 \)).
3. Compute to at least three decimal places and provide the lower and upper limits of the confidence interval rounded to two decimal places.

**Interactive Elements:**
- Send data to calculator or Excel for analysis.
- Input fields to compute and display the confidence interval limits.

**Output:**
- Lower Limit: [Input required]
- Upper Limit: [Input required]

This
Transcribed Image Text:**Study on Recovery Time from Flu** A research study investigated the effects of multivitamins and vitamin C on recovery time from a flu virus. Participants were split into two groups, each receiving different treatments and recovery times were measured. The study concluded with the following results: **Data Collected:** - **Treated with Multivitamin:** Recovery times in days: 8.5, 5.6, 8.8, 6.1, 6.1, 3.3, 8.9, 6.0, 3.3, 9.7, 6.0, 9.3, 2.3, 4.6, 5.5, 6.7, 6.6, 4.9, 10.0, 6.6 - **Treated with Vitamin C:** Recovery times in days: 6.5, 5.0, 3.2, 4.7, 3.5, 2.7, 3.8, 4.4, 4.6, 3.6, 4.0, 2.7, 3.2, 4.8, 6.3, 7.5, 6.9, 4.7, 4.8, 1.3 **Objective:** Calculate a 90% confidence interval for the difference in mean recovery times between the two groups: those treated with multivitamins (\( \mu_1 \)) and those treated with vitamin C only (\( \mu_2 \)). **Known Population Parameters:** - Standard deviation of recovery with multivitamins: 1.8 days - Standard deviation of recovery with vitamin C: 1.5 days **Instructions for Calculation:** 1. Use the collected data to compute the mean recovery times for both groups. 2. Calculate the 90% confidence interval for the difference in means (\( \mu_1 - \mu_2 \)). 3. Compute to at least three decimal places and provide the lower and upper limits of the confidence interval rounded to two decimal places. **Interactive Elements:** - Send data to calculator or Excel for analysis. - Input fields to compute and display the confidence interval limits. **Output:** - Lower Limit: [Input required] - Upper Limit: [Input required] This
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