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Bond [772]
3 years ago
7

The percent, X , of shrinkage o n drying for a certain type of plastic clay has an average shrinkage percentage :, where paramet

er : is unknown. A random sample of 45 specimens from this clay showed an average shrinking percentage of 18.4 and a standard deviation of 2.2.
Required:
a. Estimate at 5% level of significance whether the true average shrinkage percentage U: is greater than 17.5 and write your conclusion.
b. Report the p-value.
Mathematics
1 answer:
never [62]3 years ago
5 0

Answer:

a) t=\frac{18.4-17.5}{\frac{2.2}{\sqrt{45}}}=2.744    

The degrees of freedom are given by:

df=n-1=45-1=44  

The critical value for this case is t_{\alpha}=1.68 since the calculated value is higher than the critical we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly higher than 18.4

b) p_v =P(t_{(44)}>2.744)=0.0044  

Step-by-step explanation:

Information given

\bar X=18.4 represent the sample mean

s=2.2 represent the sample standard deviation

n=45 sample size  

\mu_o =17.5 represent the value to verify

\alpha=0.05 represent the significance level

t would represent the statistic

p_v represent the p value

Part a

We want to test if the true mean is higher than 17.5, the system of hypothesis would be:  

Null hypothesis:\mu \leq 17.5  

Alternative hypothesis:\mu > 17.5  

The statistic is given by:

t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}  (1)  

And replacing we got:

t=\frac{18.4-17.5}{\frac{2.2}{\sqrt{45}}}=2.744    

The degrees of freedom are given by:

df=n-1=45-1=44  

The critical value for this case is t_{\alpha}=1.68 since the calculated value is higher than the critical we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly higher than 18.4

Part b

The p value would be given by:

p_v =P(t_{(44)}>2.744)=0.0044  

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liubo4ka [24]

The statement <em>“The supplement of an acute angle is an obtuse angle.”</em> is always true because the sum of any two supplementary angles is 180°, so if one of them less than 90° (acute), then the other must be greater than 90° (obtuse)

Step-by-step explanation:

Let us revise some facts about the supplementary angles

  • Supplementary angles are two angles the sum of their measure is 180°
  • The two angles could be right angles or one of them is acute and the other is obtuse
  • The two angles can not be acute angles or obtuse angles

Let us take some examples to explain the facts above

∵ One of two supplementary angles is a right angle

∵ The measure of the right angle is 90°

∵ The sum of the measures of the supplementary angles is 180°

∴ 90 + the measure of the supplement angle = 180

- Subtract 90 from both sides

∴ The measure of the supplement angle = 90°

∴ The supplement of a right angle <u><em>must be</em></u> a right angle

∵ One of two supplementary angles is 70°

∵ Its measure less than 90°

∴ This angle is an acute angle

∵ The sum of the measures of the supplementary angles is 180°

∴ 70 + the measure of the supplement angle = 180

- Subtract 70 from both sides

∴ The measure of the supplement angle = 110°

∵ Its measure greater than 90°

∴ The supplement angle is an obtuse angle

∴ The supplement of an acute angle <u><em>must be</em></u> an obtuse angle

The two supplementary angles can not be acute angles because their sum is less than 180°

The two supplementary angles can not be obtuse angles because their sum is greater than 180°

The statement <em>“The supplement of an acute angle is an obtuse angle.”</em> is always true because the sum of any two supplementary angles is 180°, so if one of them less than 90° (acute), then the other must be greater than 90° (obtuse)

Learn more:

You can learn more about the supplementary angles in brainly.com/question/11175936

#LearnwithBrainly

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Answer:

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Step-by-step explanation:

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So the area will be 54 of the front of the book after the book is enlarged.

Hope this helps!

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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We need to find the speed of a train. The formula for speed of an object is equal to the total distance covered divided by total time taken. It can be given by :

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