Find the distance between the points (3, -1) and (4, 6).

2 answers:

6 0

$\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{3}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{6})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[4-3]^2+[6-(-1)]^2}\implies d=\sqrt{(4-3)^2+(6+1)^2} \\\\\\ d=\sqrt{50}\implies d\approx 7.07$

Nuetrik [128]4 years ago

5 0

distance formula so it is $\sqrt[]{50}$

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A random sample of 20 healthy adults was collected and their body temperatures were measured in degrees Fahrenheit. The data can

castortr0y [4]

Answer:

Step-by-step explanation:

Hello!

You need to test the hypothesis that "the average temperature for healthy adults is not equal to 98.6"

The variable of interest is

X: The body temperature of a healthy adult. (Fahrenheit)

And the parameter of interest is the population mean, μ.

The statistic hypotheses are:

H₀: μ = 98.6

H₁: μ ≠ 98.6

α:0.05

Assuming that the variable has a normal distribution you have to use a one-sample t-statistic for this test.

Attached to the answer is the data of body temperature of n=19 healthy adults. Since you didn't copy the raw data for your exercise I'll use this to answer the question.

Using the data the sample mean and standard deviation are:

X[bar]= 98.12

S= 0.69

$t= \frac{X[bar]-Mu}{\frac{S}{\sqrt{n} } } ~~t_{n-1}$

$t_{H_0}= \frac{98.12-98.6}{\frac{0.69}{\sqrt{19} } } = -3.03$

This test is two-tailed, using the critical value approach, you have the rejection region divided into two tails determined by two critical values:

$t_{n-1;\alpha /2}= t_{18;0.025}= -1.965$

$t_{n-1;1-\alpha /2}= t_{18;0.975}= 1.965$

Decision rule:

If $t_{H_0}$ ≤ -1.965 or if $t_{H_0}$ ≥ 1.965, the decision is to reject the null hypothesis.

If -1.965 < $t_{H_0}$ < 1.965, the decision is to not reject the null hypothesis.

The calculated statistic is less than the lower critical value, the decision is to reject the null hypothesis.

Using a significance level of 5%, there is enough evidence to reject the null hypothesis. Then you can conclude that the true mean body temperature for healthy adults is not equal to the traditional 98.6F.

I hope this helps!