What is the remainder when 23,870 ÷ 38

The data show systolic and diastolic blood pressure of certain people. Find the regression equation, letting the first variable

MakcuM [25]

Full Question:

The data show systolic and diastolic blood pressure of certain people. Find the regression equation, letting the first variable be the independent (x) variable. Find the best predicted diastolic pressure for a person with a systolic reading of 113. use a significance level of 0.05.

Systolic| 150 129 142 112 134 122 126 120

Diastolic| 88 96 106 80 98 63 95 64

a. What is the regression equation?

^y = __ + __x (Round to two decimal places as needed.)

b. What is the best predicted value?

^y is about __ (Round to one decimal place as needed.)

Answer:

A. yhat = a + bx = -10.64 + 0.75x

B. 74.0

Step-by-step explanation:

A. To find the regression equation here, we apply the formulas and then apply it to find the value of y given value of x:

calculate xbar and ybar which is the average of the variables:

Where n(number of values in x or y)=8

xbar = sum of x/n = 129.375

ybar = sum of y/n = 86.25

to calculate b

b= [Sum x^2 * Sum y - Sum x * Sum x*y] / [N*Sum x^2 - (Sum x)^2]

b = 0.74891

To calculate a

a = ybar - b * xbar = -10.64023

Regression equation:

y=mx+b= -10.64 + 0.75x

B. given x = 113,

y = -10.64023 + 0.74891 * 113

y= 74.0

5 0

3 years ago

The service life of a battery used in a cardiac pacemaker is assumed to be normally distributed. A random sample of 10 batteries

Nat2105 [25]

Answer:

(1) We are conducting the one-sample t-test and will be testing for the hypothesis of mean battery greater than 25 h. So, we will reject the null hypothesis for mean battery life equal to 25 hr against the alternative hypothesis for mean battery life greater than 25 hr.

(2) A 95% lower confidence interval on mean battery life is 25.06 hr.

Step-by-step explanation:

We are given that a random sample of 10 batteries is subjected to an accelerated life test by running them continuously at an elevated temperature until failure, and the following lifetimes (in hours) are obtained: 25.5, 26.1, 26.8, 23.2, 24.2, 28.4, 25.0, 27.8, 27.3, and 25.7.

Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;

P.Q. = $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample mean BAC = $\frac{\sum X}{n}$ = 26 hr

s = sample standard deviation = $\sqrt{\frac{\sum(X - \bar X)^{2} }{n-1} }$ = 1.625 hr

n = sample of batteries = 10

$\mu$ = population mean battery life

<em> Here for constructing a 95% lower confidence interval we have used a One-sample t-test statistics because we don't know about population standard deviation. </em>

(1) It is stated that the manufacturer wants to be certain that the mean battery life exceeds 25 h.

Since we are conducting the one-sample t-test and will be testing for the hypothesis of mean battery greater than 25 h. So, we will reject the null hypothesis for mean battery life equal to 25 hr against the alternative hypothesis for mean battery life greater than 25 hr.

(2) So, a 95% lower confidence interval for the population mean, $\mu$ is;

P(-1.833 < $t_9$ ) = 0.95 {As the lower critical value of t at 9

degrees of freedom is -1.833 with P = 5%}

P(-1.833 < $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ ) = 0.95

P( $-1.833 \times {\frac{s}{\sqrt{n} } }$ < ${\bar X-\mu}$ ) = 0.95

P( $\bar X-1.833 \times {\frac{s}{\sqrt{n} } }$ < $\mu$ ) = 0.95

<u>95% lower confidence interval for</u> $\mu$ = [ $\bar X-1.833 \times {\frac{s}{\sqrt{n} } }$ ]

= [ $26-1.833 \times {\frac{1.625}{\sqrt{10} } }$ ]

= [25.06 hr]

Therefore, a 95% lower confidence interval on mean battery life is 25.06 hr.

5 0

3 years ago

I appreciate any help. Trying to get the hang of these.

aliya0001 [1]

Answer:

x = 12

Step-by-step explanation:

Since the top line is equal to the bottom, you make the equation -

x + x + 4 = x + 16

You subtract an x on both sides because there is one on each side -

x + 4 = 16

Then you subtract the 4 from both sides to get x by its self, which makes

x = 12

7 0

3 years ago

Read 2 more answers

according to the general equation for conditional probability of p(an B) = 3/10 and P(B)= 3/5, what is P(A|B)

qaws [65]

The required formula is:
$P(A | B)=\frac{P(A\cap B)}{P(B)}$
Therefore the probability of A given B is:
$P(A|B)=\frac{\frac{3}{10}}{\frac{3}{5}}=\frac{3\times5}{10\times3}=\frac{1}{2}$

4 0

4 years ago

Read 2 more answers

Urgent!!!

Vladimir [108]

Answer:

A = 13 degrees

B = 65.3 degrees

C = 180 - (13 + 65.3) = 101.7 degrees

Side a = 35 km

Side b = 141.4 km

Side c = 152.4 km

4 0

2 years ago