This question is incomplete, the complete question is;
Assume that two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Which distribution is used to test the claim that women have a higher mean resting heart rate than men?
A.t
B.F
C.Normal
D. Chi-square
Answer:
A) t test
Step-by-step explanation:
A t-test uses sample information to assess how plausible it is for the population means μ1 and μ2 to be equal.
The formula for a t-statistic for two population means (with two independent samples), with unknown population variances shows us how to calculate t-test with mean and standard deviation and it depends on the assumption of having an equal variance or not.
If the variances are assumed to be not equal,
he formula is:
t = (bar X₁ - bar X₂) / √( s₁²/n₁ + s₂²/n₂ )
If the variances are assumed to be equal, the formula is:
t = (bar X₁ - bar X₂) / √ (((n₁ - 1)s₁² + (n₂ - 1)s₂²) / (n₁ + n₂ - 2)) ( 1/n₁ + 1/n₂)
it called t-test for independent samples because the samples are not related to each other, in a way that the outcomes from one sample are unrelated from the other sample.
hence option A is correct. t test
Answer:
Step-by-step explanation:
The geometric distribution represents "the number of failures before you get a success in a series of Bernoulli trials. This discrete probability distribution is represented by the probability density function:"
Let X the random variable that measures the number os trials until the first success, we know that X follows this distribution:
In order to find the expected value E(1/X) we need to find this sum:
Lets consider the following series:
And let's assume that this series is a power series with b a number between (0,1). If we apply integration of this series we have this:
(a)
On the last step we assume that 
and 
, then the integral on the left part of equation (a) would be 1. And we have:
And for the next step we have:
And with this we have the requiered proof.
And since 
we have that:
The area of a circle is π (radius²)
The area of the outer (2-ft) circle is π (2²) = 4 π square feet.
The area of the inner (1-ft) circle is π (1²) = 1 π square feet.
The inner circle covers 1/4 of the area of the outer circle.
So if the ant wanders around totally aimlessly and randomly, and there's no way to
know where he came from, where he is now, or where he's going next, and there's
an equal chance of him being <em><u>anywhere in the big circle</u></em> at any time, then there's a
<u>25% chance</u> of him being inside the small circle at any time, because 1/4 of the
total area is in there.
That's choice c).
Answer:
(-4, -5) it gives the answer in the question
Step-by-step explanation:
