The following observations are lifetimes (days) subsequent to diagnosis for individuals suffering from blood cancer. 115 182 256 419 442 462 516 739 744 789 808 865 924 984 1026 1062 1063 1165 1192 1222 1222 1251 1277 1603 1291 1358 1369 1409 1455 1479 1519 1578 1578 1599 1605 1696 1736 1799 1815 1853 1899 1925 1966 (a) Can a confidence interval for true average lifetime be calculated without assuming anything about the nature of the lifetime distribution? Explain your reasoning. [Note: A normal probability plot of the data exhibits a reasonably linear pattern O Yes, the range is sufficiently large enough for the confidence interval to be reasonable. Yes, the sample size is large enough for the confidence interval to be reasonable. O No, we need to assume that the population is normally distributed. O No, the sample size is not large enough for the confidence interval to be reasonable. O No, the range is not large enough for the confidence interval to be reasonable. (b) Calculate and interpret a confidence interval with a 99% confidence level for true average lifetime. [Hint: x = 1192.0 and s = 506.5.] (Round your answers to one decimal place.) Interpret the resulting interval. O we are 99% confident that this interval does not contain the true population mean. We are 99% confident that the true population mean lies below this interval. We are 99% confident that this interval contains the true population mean. O we are 99% confident that the true population mean lies above this interval.

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Please solve (b) & show the work needed for both (a) & (b), thanks!!

### Observations of Lifetimes (Days) for Individuals with Blood Cancer

The following data represents the number of days individuals lived after being diagnosed with blood cancer:

```
115, 182, 256, 419, 462, 516, 739, 744, 789, 808, 
865, 924, 984, 1026, 1062, 1165, 1192, 1222, 1222, 1251, 
1277, 1291, 1336, 1455, 1479, 1519, 1578, 1578, 1599, 
1603, 1605, 1679, 1815, 1899, 1925, 1966
```

#### (a) Confidence Interval Feasibility

*Question:* Can a confidence interval for the true average lifetime be calculated without assuming anything about the nature of the lifetime distribution? Explain your reasoning.

*Options:*
1. Yes, the range is sufficiently large for the confidence interval to be reasonable.
2. Yes, the sample size is large enough for the confidence interval to be reasonable.
3. No, we need to assume that the population is normally distributed.
4. No, the sample size is not large enough for the confidence interval to be reasonable.
5. No, the range is not large enough for the confidence interval to be reasonable.

*Correct Answer:* Yes, the sample size is large enough for the confidence interval to be reasonable.

*Explanation:* A normal probability plot of the data exhibits a reasonably linear pattern, indicating that the sample size can be considered adequate for constructing a confidence interval.

#### (b) Calculating the Confidence Interval

*Task:* Calculate and interpret a confidence interval with a 99% confidence level for the true average lifetime.  
*Hint:* Mean (\(\bar{x}\)) = 1192.0 days, Standard deviation (s) = 506.5 days.  
*Instructions:* Round your answers to one decimal place.

*Answer:*   
Confidence Interval: ( ___ , ___ )

*Interpretation Options:*
1. We are 99% confident that this interval does not contain the true population mean.
2. We are 99% confident that the true population mean lies below this interval.
3. We are 99% confident that this interval contains the true population mean.
4. We are 99
Transcribed Image Text:### Observations of Lifetimes (Days) for Individuals with Blood Cancer The following data represents the number of days individuals lived after being diagnosed with blood cancer: ``` 115, 182, 256, 419, 462, 516, 739, 744, 789, 808, 865, 924, 984, 1026, 1062, 1165, 1192, 1222, 1222, 1251, 1277, 1291, 1336, 1455, 1479, 1519, 1578, 1578, 1599, 1603, 1605, 1679, 1815, 1899, 1925, 1966 ``` #### (a) Confidence Interval Feasibility *Question:* Can a confidence interval for the true average lifetime be calculated without assuming anything about the nature of the lifetime distribution? Explain your reasoning. *Options:* 1. Yes, the range is sufficiently large for the confidence interval to be reasonable. 2. Yes, the sample size is large enough for the confidence interval to be reasonable. 3. No, we need to assume that the population is normally distributed. 4. No, the sample size is not large enough for the confidence interval to be reasonable. 5. No, the range is not large enough for the confidence interval to be reasonable. *Correct Answer:* Yes, the sample size is large enough for the confidence interval to be reasonable. *Explanation:* A normal probability plot of the data exhibits a reasonably linear pattern, indicating that the sample size can be considered adequate for constructing a confidence interval. #### (b) Calculating the Confidence Interval *Task:* Calculate and interpret a confidence interval with a 99% confidence level for the true average lifetime. *Hint:* Mean (\(\bar{x}\)) = 1192.0 days, Standard deviation (s) = 506.5 days. *Instructions:* Round your answers to one decimal place. *Answer:* Confidence Interval: ( ___ , ___ ) *Interpretation Options:* 1. We are 99% confident that this interval does not contain the true population mean. 2. We are 99% confident that the true population mean lies below this interval. 3. We are 99% confident that this interval contains the true population mean. 4. We are 99
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