Body Temperature The given expression is used for determining the likelihood that the average (mean) human body temperature is different from the value of 98.6°F that is commonly used. Find the given value and round the result to two decimal places.


(98.2 - 98.6) / (0.62 / sqrt(106) )

Verified step by step guidance

1. Identify the components of the expression: the numerator is the difference between the sample mean and the population mean (98.2 - 98.6), and the denominator is the standard error of the mean, which is the sample standard deviation (0.62) divided by the square root of the sample size (106).
2. Calculate the numerator: Subtract the population mean (98.6) from the sample mean (98.2) to find the difference.
3. Calculate the denominator: First, find the square root of the sample size (106). Then, divide the sample standard deviation (0.62) by this square root value to find the standard error.
4. Form the test statistic: Divide the result from the numerator by the result from the denominator. This will give you the test statistic, which is a t-score in this context.
5. Round the test statistic to two decimal places to obtain the final value, which represents the likelihood that the average human body temperature is different from 98.6°F.

Key Concepts

Hypothesis Testing

Hypothesis testing is a statistical method used to make decisions about the population based on sample data. It involves comparing the sample mean to a known value, such as 98.6°F, to determine if there is a significant difference. This process helps in assessing whether observed data can be attributed to random chance or if there is evidence of a true effect.

Standard Error

Standard error measures the variability of a sample mean from the population mean. It is calculated by dividing the sample standard deviation by the square root of the sample size, as seen in the expression (0.62 / sqrt(106)). A smaller standard error indicates that the sample mean is a more accurate reflection of the population mean, which is crucial for hypothesis testing.

Z-Score

A Z-score represents the number of standard deviations a data point is from the mean. In the given expression, (98.2 - 98.6) / (0.62 / sqrt(106)), the Z-score is used to determine how far the sample mean of 98.2°F deviates from the hypothesized mean of 98.6°F. Calculating the Z-score helps in assessing the likelihood of observing such a sample mean under the null hypothesis.