Someone Please help me. I don't understand how to do this. I need 34 points by Friday

Mkey [24]

At 13% significance level, there isn't enough evidence to prove the administrators to claim that the mean score for the state's eighth graders on this exam is more than 280.

<h3>How to state hypothesis conclusion?</h3>

We are given;

Sample size; n = 78

population standard deviation σ = 37

Sample Mean; x' = 280

Population mean; μ = 287

The school administrator declares that mean score is more (bigger than) 280. Thus, the hypotheses is stated as;

Null hypothesis; H₀: μ > 280

Alternative hypothesis; Hₐ: μ < 280

This is a one tail test with significance level of α = 0.13

From online tables, the critical value at α = 0.13 is z(c) = -1.13

b) Formula for the test statistic is;

z = (x- μ)/(σ/√n)

z = ((280 - 287) *√78 )/37

z = -1.67

c) From online p-value from z-score calculator, we have;

P[ z > 280 ] = 0.048

d) The value for z = -1.67 is smaller than the critical value mentioned in problem statement z(c) = - 1.13 , the z(s) is in the rejection zone. Therefore we reject H₀

e) We conclude that at 13% significance level, there isn't enough evidence to prove the administrators to claim that the mean score for the state's eighth graders on this exam is more than 280.

Read more about Hypothesis Conclusion at; brainly.com/question/15980493

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1 year ago

Help me Please....................

MakcuM [25]

9514 1404 393

Answer:

1.3363

Step-by-step explanation:

The basic idea here is to find an expression for the direction vector between a point on L1 and a point on L2. Then, solve for the points on L1 and L2 that make that vector perpendicular to both lines L1 and L2. (The dot product of direction vectors is zero.) The distance between the points found is the shortest distance between the lines.

__

Let P be a point on L1. Then the parametric equation for P is ...

P = (6t, 0, -t) . . . . . . origin + t × direction vector

Let Q be a point on L2. The direction vector for L2 is given by the difference between the given points. It is (4-1, 1-(-1), 6-1) = (3, 2, 5). Then the parametric equation for Q is ...

Q = (3s+1, 2s-1, 5s+1) . . . . (1, -1, 1) + s × direction vector

The direction vector for PQ is ...

Q -P = (3s+1-6t, 2s-1, 5s+1+t)

The dot product of this and the two lines' direction vectors will be zero:

(3s+1-6t, 2s-1, 5s+1+t)·(6, 0, -1) = 0 = 13s -37t +5 . . . perpendicular to L1

(3s+1-6t, 2s-1, 5s+1+t)·(3, 2, 5) = 0 = 38s -13t +6 . . . perpendicular to L2

The solution to these equations is ...

s = -157/1237

t = 112/1237

Then (Q-P) becomes (94, -1551, 564)/1237, and its length is ...

|PQ| = √(94² +1551² +564²)/1237 ≈ 1.3363

The distance between the two lines is about 1.3363 units.