Answer :
Final answer:
The best point estimate of the mean body temperature is 98.1. The 99% confidence interval estimate of the mean body temperature is 97.784 to 98.416, which does not contain 98.6. The sample suggests that the use of 98.6 as the mean body temperature is not supported by the data.
Explanation:
a) The best point estimate of the mean body temperature of all healthy humans can be found using the sample mean, which is denoted by x. In this case, x = 98.1. Therefore, the best point estimate is 98.1.
b) To construct a 99% confidence interval estimate of the mean body temperature, we will use the formula: CI = x ± (t * (s/√n)). In this case, x = 98.1, s = 0.56, n = 103, and the t-value for a 99% confidence level with 102 degrees of freedom is 2.626. Plugging these values into the formula, we get a confidence interval of 97.784 to 98.416. Since 98.6 is not within this interval, the sample suggests that the use of 98.6 as the mean body temperature is not supported by the data.
c) The confidence interval estimate of the population mean is 97.784 < μ < 98.416.
Answer:
98.1, No does not contain, yes contains.
Step-by-step explanation:
Given that
sample size n =103
Sample mean = 98.1
sample std dev s = 0.56
a) the best point estimate of the mean body temperature of all healthy humans = sample mean =98.1
b) 99% confidence interval estimate of the mean body temperature of all healthy humans
We can use Z critical since sample size is large though sigma is not known
99% CI = [tex](98.1-\frac{0.56}{\sqrt{103} },98.1+\frac{0.56}{\sqrt{103} } )\\=(98.045, 98.155)[/tex]
This does not contain 98.6
This sample does not represent the population, i.e. may be biased sample.
c) CI of population mean
= populaiton mean + /- margin of error
=(98.545, 98.656)
Yes contains 98.6
