Match each exponential expression with its value

Researchers randomly divided 500 volunteers into two equal-sized groups. One group spent 6 months on the Paleo diet. A control g

gtnhenbr [62]

Answer:

$p_v =P(t_{(498)}>1.356)=0.088$

And we can use the following excel code to find it: "=1-T.DIST(1.356,498,TRUE)"

Step-by-step explanation:

Data given and notation

$\bar X_{P}=7$ represent the mean for the sample Paleo

$\bar X_{C}=5$ represent the mean for the sample Control

$s_{P}=20$ represent the sample standard deviation for the sample Paleo

$s_{C}=12$ represent the sample standard deviation for the sample Control

$n_{P}=250$ sample size selected Paleo

$n_{C}=250$ sample size selected Control

$\alpha$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the Paleo diet provides more weight control than the control treatment, the system of hypothesis would be:

Null hypothesis: $\mu_{P}-\mu_{C}\leq 0$

Alternative hypothesis: $\mu_{P}-\mu_{C}>0$

We don't know the population deviations, so for this case is better apply a t test to compare means, and the statistic is given by:

$t=\frac{(\bar X_{P}-\bar X_{C})-12}{\sqrt{\frac{s^2_{P}}{n_{P}}+\frac{s^2_{C}}{n_{C}}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other".

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{(7-5)-0}{\sqrt{\frac{20^2}{250}+\frac{12^2}{250}}}}=1.356$

P-value

The first step is calculate the degrees of freedom, on this case:

$df=n_{P}+n_{C}-2=250+250-2=498$

Since is a one side right test the p value would be:

$p_v =P(t_{(498)}>1.356)=0.088$

And we can use the following excel code to find it: "=1-T.DIST(1.356,498,TRUE)"

8 0

3 years ago

If a plant grows 1/4 cm everyday for 21 days, what is the total amount of growth PLS HELP

KiRa [710]

5 inches and 1 centimeters

6 0

4 years ago

A man starts walking north at 2 ft/s from a point P. Five minutes later a woman starts walking south at 3 ft/s from a point 500

timurjin [86]

<span>4.98 ft/s Let's determine the distance between the man and the woman for the moment that she's been walking 15 minutes. For this you can create a right triangle where one leg is 500 ft long (the east west difference between their locations) and the other leg is (distance man walked for 20 minutes + distance woman walked for 15 minutes). So Distance man walked = 20 min * 60 s/min * 2 ft/s = 2400 ft. Distance woman walked = 15 min * 60 s/min * 3 ft/s = 2700 ft. So the north south different in the man and woman's location is 2400+2700 = 5100 ft and will be increasing by 5 ft/sec. Creating a function of time (in seconds) for the distance the two people are apart is f(t) = sqrt(500^2 + (5100 + 5t)^2) where t = number of seconds from the 15 minutes the woman has been walking. For rate of change, you want the first derivative of the function. So let's calculate it. f(t) = sqrt(500^2 + (5100 + 5t)^2) f(t) = sqrt((5100 + 5t)^2 + 250000) f'(t) = d/dt[ sqrt((5100 + 5t)^2 + 250000) ] f'(t) = 0.5((5t + 5100)^2 + 250000)^(-0.5) * d/dt[ (5t + 5100)^2 + 250000 ] f'(t) = d/dt[ (5t + 5100)^2 ] / (2 * sqrt((5t + 5100)^2 + 250000)) f'(t) = 2(5t + 5100) * d/dt[ 5x + 5100 ]/(2 * sqrt((5t + 5100)^2 + 250000)) f'(t) = 5(5t + 5100/sqrt((5t + 5100)^2 + 250000) f'(t) = (25t + 25500)/sqrt((5t + 5100)^2 + 250000) Now calculate f'(t) for t = 0. So f'(t) = (25t + 25500)/sqrt((5t + 5100)^2 + 250000) f'(0) = (25*0 + 25500)/sqrt((5*0 + 5100)^2 + 250000) f'(0) = 25500/sqrt((5100)^2 + 250000) f'(0) = 25500/sqrt(26010000 + 250000) f'(0) = 25500/sqrt(26260000) f'(0) = 25500/5124.45119 f'(0) = 4.976142626 ft/sec So the man and woman are moving away from each other at the rate of 4.98 ft/s.</span>

8 0

4 years ago

20 points PLEASE HELPPP!!!

stira [4]

Answer:

1. total area = 135mi²

Step-by-step explanation:

hope this helps :)