MATHEMATICS COLLEGE

A random sample of size 13 is selected from men with hypertension. For each person, systolic blood pressure was measured right before and one hour after taking the medicine. The mean reduction of the blood pressures was 10.1 and the standard deviation of the difference was 11.2. Test if there is sufficient evidence to conclude that the hypertension medicine lowered blood pressure. What is the value of the test statistic (round off to second decimal place)

Answers

Answer 1

Answer:

Yes, hypertension drugs lowers blood pressure.

Step-by-step explanation:

Claim: The hypertension medicine lowered blood pressure.

The null and alternative hypothesis is

H0:\mu_{d}\geq 0

H1:\mu_{d}< 0

Level of significance = 0.05

Sample size = n = 13

Sample mean of difference = \bar{d} = 10.1

Sample standard deviation of difference = s_{d} = 11.2

Test statistic is

t=\frac{\bar{d}}{s_{d}/\sqrt{n}}

t = ((10.1) / (11.2 /squre root of 13)) = 3.251

Degrees of freedom = n - 1 = 13 - 1 = 12

Critical value =2.179( Using t table)

Test statistic | t | > critical value we reject null hypothesis.

In Conclusion: The hypertension medicine lowered blood pressure

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PhD’s in Engineering. The National Science Foundation reports that 70% of the U.S. graduate students who earn PhD degrees in engineering are foreign nationals. Consider the number Y of foreign students in a random sample of 25 engineering students who recently earned their PhD.a) Find the probability that there are exactly 10 foreign students in your sample – use equation for thisb) Find the probability that there are less than or equal to 5 foreign students in your sample andc) Find the mean and standard deviation for Y

Answers

Answer:

a) P(Y=10)=0.0013

b) P(Y≤5)=0.00000035

c) Mean = 17.5

S.D. = 2.29

Step-by-step explanation:

We can model this as a binomial random variable with n=25 and p=0.7.

The probability that k students from the sample are foreign students can be calculated as:

$P(y=k) = \dbinom{n}{k} p^(k)(1-p)^(n-k)\n\n\nP(y=k) = \dbinom{25}{k} 0.7^(k) 0.3^(25-k)\n\n\n$

a) Then, for Y=10, the probability is:

$P(y=10) = \dbinom{25}{10} p^(10)(1-p)^(15)=3268760*0.0282475249*0.0000000143\n\n\nP(y=10)=0.0013\n\n\n$

b) We have to calculate the probability P(Y≤5)

$P(y\leq5)=P(Y=0)+P(Y=1)+...+P(Y=5)\n\n\nP(x=0) = \dbinom{25}{0} p^(0)(1-p)^(25)=1*1*0=0\n\n\nP(y=1) = \dbinom{25}{1} p^(1)(1-p)^(24)=25*0.7*0=0\n\n\nP(y=2) = \dbinom{25}{2} p^(2)(1-p)^(23)=300*0.49*0=0.0000000001\n\n\nP(y=3) = \dbinom{25}{3} p^(3)(1-p)^(22)=2300*0.343*0=0.0000000025\n\n\nP(y=4) = \dbinom{25}{4} p^(4)(1-p)^(21)=12650*0.2401*0=0.0000000318\n\n\nP(y=5) = \dbinom{25}{5} p^(5)(1-p)^(20)=53130*0.16807*0=0.0000003114\n\n\n\n$

$P(y\leq5)=0+0+0.0000000001+0.0000000025+0.0000000318+0.00000031\n\nP(y\leq5)= 0.00000035$

c) The mean and standard deviation for this binomial distribution can be calculated as:

$\mu=np=25\cdot 0.7=17.5\n\n\sigma=√(np(1-p))=√(25\cdot0.7\cdot0.3)=√(5.25)=2.29$

Can someone help me translate this into a mathematical notation One fourth of three times a number is five

Answers

Answer:

3x/4 = 5

Step-by-step explanation:

If minor arc AB measures 9 inches, what is the length of the radius of circle C?

Answers

Answer:

12 inches

i hope this helped

Jordan spent three hours at a local farm how many minutes did you spend at the farm?

Answers

Answer:

180 minutes.

Step-by-step explanation:

For every hour is 60 minutes. 60 x 3 = 180

Answer:I spent more time at the farm because I got there before Jordan got there.

Step-by-step explanation:

In a relay race, Jill runs 250 meters in 1.5 minutes. She hands the baton to John, who walks for 3 minutes at a rate of 70 meters per minute. Finally, Suzy sprints the last 100 meters in 15 seconds. What distance is traveled in this relay

Answers

9514 1404 393

Answer:

560 m

Step-by-step explanation:

Jill's distance is given as 250 m.

John's distance can be computed as ...

distance = speed × time = (70 m/min)(3 min) = 210 m

Suzy's distance is given as 100 m.

Then the total distance is ...

250 m + 210 m + 100 m = 560 m

The distance traveled is 560 m in this relay.

HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

the correct answer is marked (1/2)

Step-by-step explanation:

The average rate of change is the slope of the line between the two points at the ends of the interval.

m = (g(3) -g(-4))/(3 -(-4))

The values of the function we need are ...

g(3) = 5/(3-1) +2 = 2.5 +2 = 4.5

g(-4) = 5/(-4-1) +2 = -1 +2 = 1

So, the slope is ...

m = (4.5 -1)/7 = 3.5/7 = 1/2

The average rate of change is 1/2.

_____

On the attached graph, that value shows up as the coefficient of x in the equation of the line through the two points.

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