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Ipatiy [6.2K]
2 years ago
5

Integrated circuits consist of electric channels that are etched onto silicon wafers. A certain proportion of circuits are defec

tive because of "undercutting," which occurs when too much material is etched away so that the channels, which consist of the unetched portions of the wafers, are too narrow. A redesigned process, involving lower pressure in the etching chamber, is being investigated. The goal is to reduce the rate of undercutting to less than 5%. Out of the first 1000 circuits manufactured by the new process, only 35 show evidence of undercutting. Can you conclude that the goal has been met?
Mathematics
1 answer:
stiks02 [169]2 years ago
5 0

Answer:

We can conclude that the rate of undercutting is less than 5% and the goal has been met.

Step-by-step explanation:

We have a goal of a rate of 5% or lower of defects. We took a sample and now we have to perform an hypothesis test of the proportions to conclude (or not) that the rate of defects is below 5%.

The null and alternative hypothesis are:

H_0: \pi\geq0.05\\\\H_1: \pi

The significance level is defined as 0.05.

The sample proportion is

p=35/1000=0.035

The standard deviation is

\sigma=\sqrt{\frac{\pi(1-\pi)}{N} }= \sqrt{\frac{0.05(1-0.05)}{1000} }=0.007

We can calculate the statistic z-value as

z=\frac{p-\pi+0.5/N}{\sigma} =\frac{0.035-0.05+0.5/1000}{0.007}= \frac{-0.0145}{0.007}= -2.07

The p-value for this test statistic is

P(z

The P-value (0.02) is smaller than the significance level (0.05), so the effect is significant. There is enugh evidence to reject the null hypothesis.

We can conclude that the rate of undercutting is less than 5% and the goal has been met.

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2x/3=8

2x=24

x=12

It takes Molly 12 minues to run one mile.


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3 years ago
For what value of x is r(x)= -21??
Naily [24]

Answer:

Rx= - 21

Rx/r= - 21/r

X=-21/r

4 0
1 year ago
What number comes next in the series? 31, 1031, 402, 16, ____
spin [16.1K]

Answer:

Another person already answered this question. Their name is writersparadise. I give all credit to him/her for this answer.

Step-by-step explanation:

There could be many answers for this question. In general, the number that comes after 16 is a number with 8 as the sum of its digits.

Explanation:

1st number 31 – Sum of digits is 3 + 1 = 4  

2nd number 1031 – Sum of digits is 1 + 0 + 3 + 1 = 5

3rd number 402 – Sum of digits is 4 + 0 + 2 = 6

4th number 16 – Sum of digits is 1 + 6 = 7

Therefore, the missing number could be the single digit number 8 or any of the two-digit numbers 17, 26, 35, 44, 53, 62, 71 or 80. It could also be a bigger number with the digits of any of the given two-digit numbers and 0 for the other digits such as 260 or 7001.

Read more on Brainly.in - https://brainly.in/question/3032926#readmore

4 0
3 years ago
If x+ 1/x=8, find x^2+ 1/x^2​
Paraphin [41]

Dude please give me brainliest please :)
Also here’s the answer

6 0
2 years ago
Paul owns a mobile wood-fired pizza oven operation. A couple of his clients complained about his dough at a recent catering, so
Makovka662 [10]

Answer: B. Do not reject H0, we cannot conclude the proportion of customer complaints is more for the old dough

Step-by-step explanation:

This is a test of 2 population proportions. Let 1 and 2 be the subscript for the old and the new dough players. The population proportions of customer complaints with the old and new dough would be p1 and p2

P1 - P2 = difference in the proportion of customer complaints with the old and new dough.

The null hypothesis is

H0 : p1 ≥ p2

pm - pw ≥ 0

The alternative hypothesis is

Ha : p1 < p2

p1 - p2 < 0

it is a left tailed test

Sample proportion = x/n

Where

x represents number of success(number of complaints)

n represents number of samples

For old dough

x1 = 6

n1 = 385

P1 = 6/385 = 0.016

For new dough,

x2 = 16

n2 = 340

P2 = 16/340 = 0.047

The pooled proportion, pc is

pc = (x1 + x2)/(n1 + n2)

pc = (6 + 16)/(385 + 340) = 0.03

1 - pc = 1 - 0.03 = 0.97

z = (Pm - Pw)/√pc(1 - pc)(1/nm + 1/nw)

z = (0.016 - 0.047)/√(0.03)(0.97)(1/385 + 1/340) = - 0.031/√0.00553857907

z = - 0.42

Since it is a left tailed test, we would find the p value for the area to the left of the z score. From the normal distribution table,

p value = 0.337

For a 95% confidence level, the significant level, alpha is

1 - 0.95 = 0.05

Since 0.05 < 0.337, we would accept the null hypothesis

Therefore, Do not reject H0, we cannot conclude the proportion of customer complaints is more for the old dough

7 0
3 years ago
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