Scrapie is a degenerative disease of the nervous system. A study on the substance IDX as a treatment for scrapie used 28 infected hamsters as subjects. Fourteen were chosen at random and injected with IDX, while the other 14 were left untreated. The researchers recorded how long each hamster lived and reported the following:

- All infected control hamsters had died by 95 days after infection (mean ± SEM = 88 ± 1.68).
- IDX-treated hamsters lived up to 110 days (mean ± SEM = 100.2 ± 2.43).

Readers should note that SEM stands for the standard error of the mean.

(a) For the group injected with IDX, find:
- The mean: [tex]z = 100.2[/tex]
- The standard deviation: [tex]x = 9.0922[/tex]

(b) For the untreated group, find:
- The mean: [tex]x = 88[/tex]
- The standard deviation: [tex]8 = 8.8897[/tex]

This statistics-related question illustrates the use of mean and standard deviation to interpret data from a study about treating hamsters with a degenerative disease, Scrapie, using the IDX substance. The treated group lived longer with a mean of 88 days and standard deviation of 8.8897, compared with the untreated group's mean of 100.2 days and standard deviation of 9.0922.

Explanation:

The question pertains to a study on the effectiveness of the substance IDX as a treatment for the degenerative disease, Scrapie, in hamsters. The given data is about the lifespan of both infected control hamsters (untreated) and those treated with IDX. Before we proceed, you should know that 'mean' signifies the average, and 'SEM' stands for Standard Error of the Mean, which provides an estimate of the variability of the measurements.

For the group injected with IDX, the mean or average lifespan is denoted as 'z' and equates to 88 days. The Standard Deviation, given as 'x', is calculated as 8.8897. As for the untreated group, the mean lifespan is given as 'x' and is 100.2 days. This group’s Standard Deviation, denoted as '8', equals 9.0922 days. These metrics indicate substantial differences in both the average lifespan and variability in lifespan between treated and untreated hamsters.

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