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Stels [109]
3 years ago
5

What is the value of f(x) when x= -3

Mathematics
1 answer:
KIM [24]3 years ago
6 0

Answer:f=-3

Step-by-step explanation:

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To test Upper H 0​: muequals50 versus Upper H 1​: muless than50​, a random sample of size nequals23 is obtained from a populatio
natta225 [31]

Answer:

Step-by-step explanation:

Hello!

1)

<em>To test H0: u= 50 versus H1= u < 50, a random sample size of n = 23 is obtained from a population that is known to be normally distributed. Complete parts A through D. </em>

<em> A) If  ¯ x = 47.9  and s=11.9, compute the test statistic .</em>

For thistest the corresponsing statistis is a one sample t-test

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

t_{H_0}= \frac{47.9-50}{\frac{11.9}{\sqrt{23} } } = -0.846= -0.85

B) If the researcher decides to test this hypothesis at the a=0.1 level of significance, determine the critical value(s).

This test is one-tailed to the left, meaning that you'll reject the null hypothesis to small values of the statistic. The ejection region is defined by one critical value:

t_{n-1;\alpha }= t_{22;0.1}= -1.321

Check the second attachment. The first row shows α= Level of significance; the First column shows ν= sample size.

The t-table shows the values of the statistic for the right tail. P(tₙ≥α)

But keep in mind that this distribution is centered in zero, meaning that the right and left tails are numerically equal, only the sign changes. Since in this example the rejection region is one-tailed to the left, the critical value is negative.

C) What does the distribution graph appear like?

Attachment.

D) Will the researcher reject the null hypothesis?

As said, the rejection region is one-tailed to the right, so the decision rule is:

If t_{H_0} ≤ -1.321, reject the null hypothesis.

If t_{H_0} > -1.321, do not reject the null hypothesis.

t_{H_0}= -0.85, the decision is to not reject the null hypothesis.

2)

To test H0​: μ=100 versus H1​:≠​100, a simple random sample size of nequals=24 is obtained from a population that is known to be normally distributed. Answer parts​ (a)-(d).

a) If x =104.2 and s=9.6, compute the test statistic.

For this example you have to use a one sample t-test too. The formula of the statistic is the same:

t_{H_0}= \frac{X[bar]-Mu}{\frac{S}{\sqrt{n} } } = \frac{104.2-100}{\frac{9.6}{\sqrt{24} } = } = 2.143

b) If the researcher decides to test this hypothesis at the α=0.01 level of​ significance, determine the critical values.

This hypothesis pair leads to a two-tailed rejection region, meaning, you'll reject the null hypothesis at either small or big values of the statistic. Then the rejection region is divided into two and determined by two critical values (the left one will be negative and the right one will be positive but the module of both values will be equal).

t_{n-1;\alpha/2 }= t_{23; 0.005}= -2.807

t_{n-1;1-\alpha /2}= t_{23;0.995}= 2.807

c) Draw a​ t-distribution that depicts the critical​ region(s). Which of the following graphs shows the critical​ region(s) in the​t-distribution?

Attachment.

​(d) Will the researcher reject the null​ hypothesis?

The decision rule for the two-tailed hypotheses pair is:

If t_{H_0} ≤ -2.807 or if t_{H_0} ≥ 2.807, reject the null hypothesis.

If -2.807 < t_{H_0} < 2.807, do not reject the null hypothesis.

t_{H_0}= 2.143 is greater than the right critical value, the decision is to reject the null hypothesis.

Correct option:

B. The researcher will reject the null hypothesis since the test statistic is not between the critical values.

3)

Full text in attachment. The sample size is different by 2 but it should serve as a good example.

H₀: μ = 20

H₁: μ < 20

a) n= 18, X[bar]= 18.3, S= 4, Compute statistic.

t_{H_0}= \frac{X[bar]-Mu}{\frac{S}{\sqrt{n} } }= \frac{18.3-20}{\frac{4}{\sqrt{18} } } = -1.80

b) The rejection region in this example is one-tailed to the left, meaning that you'll reject the null hypothesis to small values of t.

Out of the three graphics, the correct one is A.

c)

To resolve this you have to look for the values in the t-table that are the closest to the calculated t_{H_0}

Symbolically:

t_{n-1;\alpha_1 } \leq t_{H_0}\leq t_{n-1;\alpha _2}

t_{H_0}= -1.80

t_{17; 0.025 }= -2.110

t_{17;0.05}= -1.740

Roughly defined you can say that the p-value is the probability of obtaining the value of t_{H_0}, symbolically: P(t₁₇≤-1.80)

Under the distribution the calculated statistic is between the values of -2.110 and -1.740, then the p-value will be between their cumulated probabilities:

A. 0.025 < p-value < 0.05

d. The researcher decides to test the hypothesis using a significance level of α: 0.05

Using the p-value approach the decision rule is the following:

If p-value ≤ α, reject the null hypothesis.

If p-value > α, do not reject the null hypothesis.

We already established in item c) that the p-value is less than 0.05, so the decision is to reject the null hypothesis.

Correct option:

B. The researcher will reject the null hypothesis since the p-value is less than α.

I hope this helps!

6 0
3 years ago
On a hiking trip, Melissa notes that she hikes about 16 kilometers every 2.5 hours. If she continues at this rate, about how man
svp [43]

Answer:

so if she hike 12 km every 4 hours, how many km could she hike in 6 hours.

first u have to find the equation. 12 km=4hours

? =6hours

and then you have to multiply 12 km by 6 hours and divide the results by 4 which is 12×6÷4. the final answer will be 18 kilometers.

Step-by-step explanation:

Sorry if its wrong

5 0
3 years ago
ILL MARK BRAINIEST IF YOU DO THIS CORRECTLY!!!
ehidna [41]

Answer:

76 percent done.

Step-by-step explanation:

Reasoning for this if its 76/100 you know that it will be 76. Or im Just got confused.

7 0
2 years ago
The height of a cylinder is equal to the diameter of the base What expression represents the volume of the cylinder, in cubic un
Sveta_85 [38]

Answer: 3 units

Step-by-step explanation:

the volume of a cone C = πr²h/3

C = 18π, h =2x, r = diameter/2 = 2x/2 =x

18π = π* x²* 2x/3

divide through by π

18 = x² * 2x/3

multiply through by 3

54 = 2x³

divide through by 2

27 = x³

x =∛27 = 3

x = 3 units = radius

4 0
3 years ago
GEOMETRY: TANGENTS, SECANTS, AND CHORDS<br> can someone solve this with written work?
Dmitry [639]
Through a geometric proof, 2(55x-1) = 107x+1
110x-2=107x+1
3x=3
x=1
Angle DEF is 54 degrees.
 
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3 years ago
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