Final answer:
To find the total height of 25 individuals with a mean height of 70 inches, one multiplies the mean height by the number of individuals. The standard deviation is calculated by taking the square root of the variance, and the coefficient of variation is the standard deviation divided by the mean, and then multiplied by 100 to get a percentage.
Step-by-step explanation:
To answer the student's question about the total height of 25 individuals:
- Total height can be calculated by multiplying the mean height by the number of individuals. Therefore, Total Height = Mean Height × Number of Individuals = 70 inches × 25 = 1750 inches.
- To compute the standard deviation, we take the square root of the variance. Thus, Standard Deviation = √Variance = √74 ≈ 8.60 inches (to two decimal places).
- The coefficient of variation (CV) is the standard deviation divided by the mean, expressed as a percentage. CV = (Standard Deviation / Mean) × 100 = (8.60 / 70) × 100 ≈ 12.3% (to one decimal place).
To illustrate the concept using the provided examples:
- For the basketball team players with a standard deviation of 1.8 inches and a p-value almost zero, the null and alternative hypotheses would be:
H0: μ = 73 (The mean height is equal to 73 inches)
H1: μ < 73 (The mean height is less than 73 inches)
A p-value almost zero indicates strong evidence against the null hypothesis, suggesting the mean height is less than 73 inches. - When constructing a confidence interval for a mean height using a normal distribution and a known standard deviation, the sample mean and sample size are used to determine the interval's limits.
- The concept of a z-score is to measure the number of standard deviations a data point is from the mean. For example, a height of 77 inches among basketball players with a mean of 79 and a standard deviation of 3.89 inches would have a z-score calculation based on these values.