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sdas [7]
3 years ago
12

Use the given information to find the p-value. also use a0.05 significance level and state the conclusion about the null hypothe

sis (reject the null hypothesis or fail tor rejected the null hypothesis)
With H1 : p < 3/5; the test statistic is z = -1.68

A: 0.093 ; fail to reject the null hypothesis
B: 0.0465 ; fail to reject the null hypothesis
C: 0.0465 ; reject the null hypothesis
D: 0.09535 ; fail to reject the null hypothesis

With H1 : p > 0.383, the test statistic is z = 0.41

A: 0.6591 ; fail to reject the null hypothesis
B: 0.3409 ; fail to reject the null hypothesis
C: 0.3490 ; reject the null hypothesis
D: 0.6818 ; reject the null hypothesis
Mathematics
1 answer:
omeli [17]3 years ago
5 0

Answer:

(a) C: 0.0465 ; reject the null hypothesis

(b) B: 0.3409 ; fail to reject the null hypothesis

Step-by-step explanation:

Firstly, the decision rule based on P-value to reject the null hypothesis or fail to reject the null hypothesis is given by;

  • If the P-value of test statistics is less than the level of significance, then we have sufficient evidence to reject our null hypothesis.
  • If the P-value of test statistics is more than the level of significance, then we have insufficient evidence to reject our null hypothesis due to which we fail to reject our null hypothesis.

(a) Now, we are given alternate hypothesis, H_1 : p < 3/5

Also, z test statistics is -1.68. Since this is a left tailed test, so P-value is given by;

             P-value = P(Z < -1.68) = 1 - P(Z \leq 1.68)

                           = 1 - 0.95352 = <u>0.0465</u>

Since, the P-value of test statistics is less than the level of significance as 0.0465 < 0.05, so we have sufficient evidence to reject our null hypothesis due to which <u>we reject the null hypothesis.</u>

(b) Now, we are given alternate hypothesis, H_1 : p > 0.383

Also, z test statistics is 0.41. Since this is a right tailed test, so P-value is given by;

             P-value = P(Z > 0.41) = 1 - P(Z \leq 0.41)

                           = 1 - 0.6591 = <u>0.3409</u>

Since, the P-value of test statistics is more than the level of significance as 0.3409 > 0.05, so we have insufficient evidence to reject our null hypothesis due to which <u>we fail to reject the null hypothesis.</u>

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irina [24]

Answer:

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Step-by-step explanation:

In a 30-60-90 triangle, the ratios of the side lengths of the triangle is 1:\sqrt{3} :2

Where 1 is the shortest leg, root(3) is the longer leg, and 2 is the hypotenuse.

First we can set x equals to the length of the original pole, and so the shorter leg has a length of x/3 and using the ratio of side lengths, we can find that:

\frac{x}{3} * \sqrt{3} = \frac{\sqrt{3} x}{3} = 12

Solving for x, we find that

x=\frac{36}{\sqrt{3} } = \frac{36 * \sqrt{3} }{\sqrt{3} * \sqrt{3} } = \frac{36  \sqrt{3} }{3} = 12\sqrt{3}

So the length of the original pole would be 12\sqrt{3} feet

If you found this answer helpful, please consider marking it as brainliest, or give it a thanks and a 5 star review. Thanks!

6 0
3 years ago
I don't know what the answer is to divide 180 in a ratio of 4:5:9
Karolina [17]
Hello there,

First you need to add together the numbers.
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Hope This Helps You!
Good Luck Studying :)
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Answer:

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