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Sergio [31]
3 years ago
10

When working properly, a machine that is used to makes chips for calculators does not produce more than 4% defective chips. When

ever the machine produces more than 4% defective chips, it needs an adjustment. To check if the machine is working properly, the quality control department at the company often takes samples of chips and inspects them to determine if they are good or defective. One such random sample of 200 chips taken recently from the production line contained 12 defective chips. Find the p-value to test the hypothesis whether or not the machine needs an adjustment. What would your conclusion be if the significance level is 2.5%
Mathematics
1 answer:
Anika [276]3 years ago
8 0

Answer:

The proportion of defective chips produced by the machine is more than 4% so the machine needs an adjustment.

Step-by-step explanation:

In this case we need to test whether the proportion of defective chips produced by the machine is more than 4%.

The hypothesis can be defined as follows:

<em>H</em>₀: The proportion of defective chips produced by the machine is not more than 4%, i.e. <em>p</em> ≤ 0.04.

<em>H</em>ₐ: The proportion of defective chips produced by the machine is more than 4%, i.e. <em>p</em> > 0.04.

The information provided is:

<em>X</em> = 12

<em>n</em> = 200

<em>α</em> = 0.025

The sample proportion of defective chips is:

\hat p=\frac{X}{n}\\\\=\frac{12}{200}\\\\=0.06

Compute the test statistic as follows:

z=\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n}}}\\\\=\frac{0.06-0.04}{\sqrt{\frac{0.04(1-0.04)}{200}}}\\\\=1.44

The test statistic value is 1.44.

Decision rule:

We reject a hypothesis if the p-value of a statistic is lower than the level of significance α.

Compute the <em>p</em>-value of the test:

p-value=P(Z>1.44)\\=1-P(Z

The <em>p</em>-value of the test is 0.075.

<em>p</em>-value = 0.075 > <em>α</em> = 0.025

The null hypothesis was failed to be rejected at 2.5% level of significance.

Thus, it can be concluded that the proportion of defective chips produced by the machine is more than 4% so the machine needs an adjustment.

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Step-by-step explanation:

f(x) =  - 5x - 4

\:

<u>Inverse</u>

y =  - 5x - 4

x =  - 5y - 4

x + 4 =  - 5y

y =  -  \frac{(x + 4)}{5}

{f}^{ - 1} (x) =  -  \frac{(x + 4)}{5}

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What is the minimum number of times you must throw three fair six-sided dice to ensure that the same sum is rolled twice?
Vladimir [108]
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For instance the minimum sum occurs when all three dices shows 1 (i.e. 1 + 1 + 1 = 3) and the maximum sum occurs when all three dces shows 6 (i.e. 6 + 6 + 6 = 18).

Thus, there are 16 possible sums when three six-sided dice are rolled.

Therefore, from the pigeonhole principle, <span>the minimum number of times you must throw three fair six-sided dice to ensure that the same sum is rolled twice is 16 + 1 = 17 times.

The pigeonhole principle states that </span><span>if n items are put into m containers, with n > m > 0, then at least one container must contain more than one item.

That is for our case, given that there are 16 possible sums when three six-sided dice is rolled, for there to be two same sums, the number of sums will be greater than 16 and the minimum number greater than 16 is 17.
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Each morning papa noted the birds feeding on his birdfedder . So far this month he had seen 59 blue jays ,68 black crows , 12 re
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To calculate the total you add them all together:
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Then the percentages of the blue jays that fed on his bird feeder are:
59/140 *100 = 42.143%

You want to see how many blue jays we can expect to see out of 300 birds. 
So you divide 300 by 100 to see what 1% is = 3 birds 

Then you multiply this amount (1% = 3 birds) by 42.134% which is the percentage of blue jays we can expect to see out of the 300 birds. 
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