A data set includes body temperatures of healthy adult humans for which x= 98.2 and
s=0.64 F. Complete parts a) and b) below
a) what is the best point estimate of the
mean body temperature of all healthy humans? The best point estimate is F.
b) Using the sample statistics, construct a 99% confidence interval estimate of the mean body temperature of all healthy humans. Do the confidence
interval contain 98.6 F. What does the sample suggest about the use of 98.6 as
the mean body temperature. What is the confidence interval estimate of the population mean u? F<u<F. Round to three places as needed. Do the confidence interval limits contain 98.6 F. What does this suggest about the use of 98.6 as the mean body temperature?
A data set includes 105 body temperatures of healthy adult humans for which x= 98.7°F and s= 0.64°F.
a) The best point estimate of the mean body temperature of all healthy humans is the sample mean, which is given as x = 98.2°F.
b) To construct a 99% confidence interval estimate of the mean body temperature of all healthy humans, we will use the formula:
CI = x ± (Z * (s / sqrt(n)))
where CI is the confidence interval, x is the sample mean, Z is the z-score corresponding to the desired confidence level (99% in this case), s is the sample standard deviation, and n is the sample size.
Using the given values: x = 98.2°F, s = 0.64°F, and a desired confidence level of 99%, we can find the corresponding z-score.
The z-score for a 99% confidence level is approximately 2.576.
Now, substituting the values into the formula:
CI = 98.2 ± (2.576 * (0.64 / sqrt(n)))
Since the sample size is not provided, we are unable to calculate the confidence interval or determine if it contains 98.6°F.
However, if we assume a typical sample size of around 30, the approximate confidence interval would be:
CI = 98.2 ± (2.576 * (0.64 / sqrt(30)))
CI ≈ 98.2 ± (2.576 * 0.117)
CI ≈ 98.2 ± 0.301
CI ≈ (97.899, 98.501)
Therefore, the confidence interval estimate of the population mean µ is 97.899°F to 98.501°F. Based on this confidence interval, 98.6°F is not within the range. This suggests that the sample data does not support the use of 98.6°F as the mean body temperature of all healthy humans.
To answer the questions, let's understand the concept of point estimate and confidence interval.
a) Point estimate is a single value that estimates an unknown population parameter. In this case, we want to find the best point estimate of the mean body temperature of all healthy humans.
The best point estimate of the mean body temperature can be calculated as the sample mean, x. From the given data, x=98.2 F. So, the best point estimate of the mean body temperature is 98.2 F.
b) Confidence interval estimate, on the other hand, provides a range of plausible values for the unknown population parameter. In this case, we want to construct a 99% confidence interval estimate of the mean body temperature of all healthy humans.
To construct the confidence interval, we will use the formula:
Confidence Interval = x +- (z * s/sqrt(n))
Where:
x = sample mean (98.2 F)
s = sample standard deviation (0.64 F)
n = sample size (not provided)
To calculate the confidence interval estimate, we need to know the sample size. Could you please provide the sample size?
a. The best point estimate is 98.2
b. 98.2 - 2.575 * 0.64/sqrt(n) < u< 98.2 + 2.575 * 0.64/sqrt(n)
This suggests that the mean body temperature could be lower than 98.6 ̊F.