Mathematics, 12.03.2020 06:09 Miloflippin7339

A data set includes 103103 body temperatures of healthy adult humans having a mean of 98.998.9degrees°f and a standard deviation of 0.650.65degrees°f. construct a 9999% confidence interval estimate of the mean body temperature of all healthy humans. what does the sample suggest about the use of 98.6degrees°f as the mean body temperature?

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Answer from: malissa0325

$98.9-2.62\frac{0.65}{\sqrt{103}}=98.73$

$98.9+2.62\frac{0.65}{\sqrt{103}}=99.07$

So on this case the 99% confidence interval would be given by (98.73;99.07)

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X=98.9$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s=0.65 represent the sample standard deviation

n=103 represent the sample size

Solution to the problem

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

df=n-1=103-1=102

Since the Confidence is 0.99 or 99%, the value of $\alpha=0.01$ and $\alpha/2 =0.005$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,102)".And we see that $t_{\alpha/2}=2.62$

Now we have everything in order to replace into formula (1):

$98.9-2.62\frac{0.65}{\sqrt{103}}=98.73$

$98.9+2.62\frac{0.65}{\sqrt{103}}=99.07$

So on this case the 99% confidence interval would be given by (98.73;99.07)

Answer from: tgdetwiler2905

99% confidence interval estimate of the mean body temperature of all healthy humans is between a lower limit of 98.73 °F and an upper limit of 99.07 °F.

The sample suggest a lower confidence interval (98.43 °F, 98.77 °F) about the use of 98.6 °F as the mean body temperature.

Step-by-step explanation:

Confidence interval = mean +/- margin of error (E)

mean = 98.9 °F

sd = 0.650 °F

n = 103

degree of freedom (df) = n - 1 = 103 - 1 = 102

confidence level (C)= 99% = 0.99

significance level = 1 - C = 1 - 0.99 = 0.01 = 1%

From the t-distribution table, t-value corresponding to 102 df and 1% significance level is 2.6251

E = t×sd/√n = 2.6251×0.65/√103 = 0.17 °F

Lower limit = mean - E = 98.9 - 0.17 = 98.73 °F

Upper limit = mean + E = 98.9 + 0.17 = 99.07 °F

99% confidence interval is (98.73 °F, 99.07 °F)

When the mean body temperature is 98.6 °F

Lower limit = mean - E = 98.6 - 0.17 = 98.43 °F

Upper limit = mean + E = 98.6 + 0.17 = 98.77 °F

99% confidence interval when the mean body temperature is 98.6 °F is (98.43 °F, 98.77 °F)

Answer from: Quest

15%

step-by-step explanation:

use the table and count the number of guesses that has two correct answers.

the following are two correct answers

10010, 01100, 11000

a total of 3 numbers having 2 correct guesses out of 20 questions.

probability of getting 2 correct guesses = the number of questions getting 2 correct answers / total number of questions.

= 3/20

to convert it into percent multiply by 100, we get

= 3/20 * 100

= 15%

the answer is 15%

you.

Afive question multiple-choice quiz has five choices for each answer. use the random number table pr

Answer from: Quest

a line is an defined derm because it

a)contains an infinite number of points b) can be used to create other geometric shapes c)describes something that does not have width or depth d) is a term that does not have a formal definition. a line is an undefined term because it: contains an infinite number of points.