Question: The times in days from remission induction to relapse for 52 patients with acute nonlymphoblastic leukemia who were treated on a common protocol at university and private institutions in the Pacific Northwest are shown below (data is also available

1. ( 5 points) Find the five-number summary and 80 -th percentile.
2. (5 points) Construct a stem-and-leave display and box-and-whisker plot. Comment on the graphs.
3. (5 points) Construct a frequency table using 7 intervals of equal length and \((0.5,170.5)\) as the first class interval.
4. (5 points) Construct a relative frequency histogram for the grouped data.
5. (5 points) From the frequency histogram we see that \(X\) seems to have an exponential distribution with mean \(\theta\). Calculate the sample mean \(\bar{x}\) and sample standard deviation \(s\). Do they support this belief? Explain why. Find the maximum likelihood estimate \(\hat{\theta}\) of \(\theta\) based on the above 52 observations and the exponential model.
6. (5 points) Do (a) and (b) of Exercise 6.6-6 on Page 376 of the textbook. [ Use relationship between chi-square and gamma, exponential distributions rather than the moment-generating function to do part (a). Some theorems can be found in my note.]
7. ( 5 points) Use the confidence interval obtained in (b) of Exercise 6.6-6 to construct a \(95 \%\) confidence interval for \(\theta\) based on the above 52 observations.
8. ( 5 points) Test hypotheses \(H_{0}: \theta=250\) vs. \(H_{1}: \theta>250\) with \(\alpha=0.05\) based on the 52 observations.

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