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docker41 [41]
2 years ago
6

A carpenter is making doors that are 2058 millimeters tall. If the doors are too long they must be trimmed, and if they are too

short they cannot be used. A sample of 17 doors is taken, and it is found that they have a mean of 2069 millimeters with a standard deviation of 24. Assume the population is normally distributed. Is there evidence at the 0.02 level that the doors are either too long or too short
Mathematics
1 answer:
marysya [2.9K]2 years ago
3 0

There is not enough evidence at the 0.02 level that the doors are either too long or too short. So, the null hypothesis is accepted.

<h3>How to decide whether the null hypothesis is rejected or accepted?</h3>

Using the p-value approach for the hypothesis test, whether the null hypothesis is rejected or accepted.

  • If the p-value is greater than the significance level then the null hypothesis is accepted.
  • If the p-value is less than the significance level then the null hypothesis is rejected.

<h3>Calculation:</h3>

It is given that,

Sample size n = 17

Sample mean X = 2069

Standard deviation σ = 24

Population mean  μ = 2058

Significance level α = 0.02

Hypothesis:

The null hypothesis: H0: μ = 2058

The alternative hypothesis: Ha: μ ≠ 2058

So, the z-test score for the given distribution is,

z-score = (X - μ)/(σ/√n)

On substituting,

z-score = (2069 - 2058)/(24/√17)

            = 11/5.82

            = 1.89

Thus, the p-value for the z-score of 1.89 is 0.0587 ≅ 0.06.

Since 0.06 > 0.02(significance level), the null hypothesis is accepted. So, there is no sufficient evidence that the doors are either too long or too short.

Learn more about p-value approaches for hypothesis testing here:

brainly.com/question/14805123

#SPJ4

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Abcd is a rectangle if DB=26 and DC=24 find bc
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Let's solve this problem step-by-step.

STEP-BY-STEP EXPLANATION:

Let's first establish that triangle BCD is a right-angle triangle.

Therefore, we can use Pythagoras theorem to find BC and solve this problem. Pythagoras theorem is displayed below:

a^2 + b^2 = c^2

Where c = hypotenus of right-angle triangle

Where a and c = other two sides of triangle

Now we can solve the problem by substituting the values from the problem into the Pythagoras theorem as displayed below:

Let a = BC

b = DC = 24

c = DB = 26

a^2 + b^2 = c^2

a^2 + 24^2 = 26^2

a^2 = 26^2 - 24^2

a = square root of ( 26^2 - 24^2 )

a = square root of ( 676 - 576 )

a = square root of ( 100 )

a = 10

Therefore, as a = BC, BC = 10.

If we want to check our answer, we can substitute the value of ( a ) from our answer in conjunction with the values given in the problem into the Pythagoras theorem. If the left-hand side is equivalent to the right-hand side, then the answer must be correct as displayed below:

a = BC = 10

b = DC = 24

c = DB = 26

a^2 + b^2 = c^2

10^2 + 24^2 = 26^2

100 + 576 = 676

676 = 676

FINAL ANSWER:

Therefore, BC is equivalent to 10.

Please mark as brainliest if you found this helpful! :)
Thank you and have a lovely day! <3
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