Question

In a study of 225 adults, the mean heart rate was 72 beats per minute. Assume the population of heart rates is known to be approximately normal with a standard deviation of 10 beats per minute. What is the 90% confidence interval for the mean beats per minute?

Answer 1

@mathmale

Answer 2

so you are looking for a confidence interval for \(\mu\), right? you know the underlying population is approx. normal and you know \(\sigma\) = 10. the sample size is 225 and \(\bar{x}\) = 72.

also, you know that you want a 90% confidence interval.

from the given info, what distribution does \(\bar{x}\) follow?

Answer 3

Thats one of my question aswell i forgot to add that i do not get what \[\frac{ }{ x }\]

Answer 4

is

Answer 5

\(\bar{x}\) is the sample mean. that is, it is the mean heart rate of the 225 adults sampled.

Answer 6

do you know the definition of \(\mu\)?

Answer 7

do you know the definition of \(\sigma\)?

Answer 8

your not going to like my response but i kinda of fudge through the beginning of this lesson but ill take notes now lol

Answer 9

dude, math and stats is all about definitions. if you don't know those then it's diificult to speak the language.

more than that, just how something is defined in math can have many implications. just saying, if you want to learn math, learn and understand the definitions!

Answer 10

i can probably find them in a matter of a few minutes. online school dont ya know.

Answer 11

the O symbol is the population standard deviation cant find n must be in a different lesson

Answer 12

anyhow, you'll need a kind of flow chart for these... good news! hypothesis testing will use the same flow chart.

basically, if the underlying data is approximately normal (which it almost is) then if \(\sigma\) is known and you want to test or construct a confidence interval for \(\mu\) then you use the normal distribution. if sigma is unknown, then you use the t distribution.

if you know nothing about the underlying distribution, then you are supposed to know \(\sigma\) (according to the theory) and use the normal distribution, so long as your sample size is larger than 30.

you can look up the central limit theorem... it discusses all of this.

for your problem, you'll need to use the normal distribution.

since you want a 90% confidence interval, this means \(\alpha\) = .10, which is 1 - .90 = .10

then \(\frac{\alpha}{2}\) = .05

that will lead to the z value needed in your problem. \[z_{\frac{\alpha}{2}}=1.645\]

then \[\bar{x}-z_{\frac{\alpha}{2}} \cdot \frac{\sigma}{n}<\mu<\bar{x}+z_{\frac{\alpha}{2}} \cdot \frac{\sigma}{n}\]

gives the confidence interval you seek.

sorry, gotta go. i have a student.