Question

Here are the questions in plain text format:

Find the following:
a. Z_{0.31}
b. Z_{0.47}
c. Z_{0.97}
A medical experiment on tumor growth gives the following data table:

x y
65 33
70 35
86 45
100 52
222 70

The least squares regression line was found. Using technology

Answer 1

a. Z_{0.31} = 0.1161

b. Z_{0.47} = 0.1772

c. Z_{0.97} = 1.8821

Step-by-step explanation:

In statistical analysis, Z-scores represent the number of standard deviations a particular data point is from the mean. For the given values, Z_{0.31}, Z_{0.47}, and Z_{0.97} are calculated as 0.1161, 0.1772, and 1.8821, respectively. These values indicate the position of the corresponding data points relative to the mean in terms of standard deviations.

Z-scores are a crucial tool in statistics, helping assess the relative position of data points in a distribution. They are particularly useful in identifying outliers and understanding the distribution of a dataset.

A Z-score of 0 signifies the data point is exactly at the mean, positive values indicate points above the mean, and negative values indicate points below the mean. Understanding Z-scores is fundamental for statistical analysis and hypothesis testing.