The human body maintains its internal temperature through thermoregulation, and a healthy adult has a mean body temperature of 98.6 °F. The processes of thermoregulation begin to deteriorate in older age, making it difficult to diagnose elderly patients who might have an illness.

To understand the body temperature of elderly patients, researchers randomly sampled the body temperatures of elderly patients from a large database of medical records where the body temperatures were normally distributed.

Conduct a two-tailed, one-sample t-test to determine whether the mean body temperature of the elderly patients is different from that of a healthy adult using the sample data provided in degrees Fahrenheit. Use a significance level of [tex]\alpha = 0.05[/tex].

Sample data: 96.7, 96.9, 97.0, 97.5, 97.6, 98.2, 98.3, 98.3, 99.1, 97.5

Calculate the t-statistic for this one-sample t-test. You can calculate the t-statistic by hand or use a software application to perform the calculation. Provide your answer for the t-statistic with precision to two decimal places.

The 1-statistic for this one-sample t-test can be calculated by subtracting the hypothesized value (98.6 °E) from the sample mean, dividing by the sample standard deviation divided by the square root of the sample size.

Explanation:

To calculate the 1-statistic for a one-sample t-test, you need the sample mean, the hypothesized value, the sample standard deviation, and the sample size. In this case, the sample mean is the mean body temperature of the elderly patients, the hypothesized value is the mean body temperature of a healthy adult (98.6 °E), the sample standard deviation is the standard deviation of the body temperatures of the elderly patients, and the sample size is the number of elderly patients in the sample.

Using the provided data set, we can calculate the 1-statistic as follows:

Calculate the sample mean: Add up all the body temperatures of the elderly patients and divide by the sample size.
Calculate the sample standard deviation: Subtract the sample mean from each body temperature, square the differences, add up the squared differences, divide by the sample size minus 1, and take the square root of the result.
Calculate the 1-statistic: Subtract the hypothesized value (98.6 °E) from the sample mean, divide by the sample standard deviation divided by the square root of the sample size.

By comparing the calculated 1-statistic to the critical value from the t-distribution with (sample size - 1) degrees of freedom, we can determine whether the mean body temperature of the elderly patients is significantly different from that of a healthy adult.

Learn more about one-sample t-test here:

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