Given the linear correlation coefficient r and the sample size n, determine the critical values of r and use your finding to state whether or not the given r represents a significant linear correlation. Use a significance level of 0.05. r = 0.543, n = 25

Using the principle of hypothesis testing, the correlation Coefficient is greater than the critical value. Hence, the linear correlation Coefficient value is significant.

Given the Parameters :

Recall :

Decision Region :

Critical value at T0.05, 23 = ±0.396

Comparing the critical value and correlation Coefficient :

Hence, the correlation Coefficient is significant.

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 r represents a significant linear correlation.

Step-by-step explanation:

GIven : Linear correlation coefficient: r = 0.543

Sample size: n= 25

Significance levle:

Degree of freedom : n-2 = 25-2=23

Now, we check r critical value table for value with df = 23 and .

Critical value = ±0.396  [From r critical value table]

Since r = 0.543 > 0.396, that means there is significant linear correlation.

Hence,  r represents a significant linear correlation.

option a, c,d are correct.

step-by-step explanation:

from the given figure, it is given that z is equidistant from the sides of the triangle rst, then from triangle tzb and triangle szb, we have

tz=sz(given)

bz=zb(common)

therefore, by rhs rule,δtzb ≅δszb

by cpctc, sz≅tz

also, from δctz and δasz,

tz=sz(given)

∠tcz=∠saz(90°)

by rhs rule, δctz ≅ δasz, therefore by cpctc, ∠ctz≅∠asz

also,from δasz and δzsb,

zs=sz(common)

∠zbs=∠saz=90°

by rhs rule, δasz ≅δzsb, therefore, by cpctc, ∠asz≅∠zsb

hence, option a, c,d are correct.

quit

step-by-step explanation: