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Vesna [10]
2 years ago
6

A quality control engineer is interested in estimating the proportion of defective items coming off a production line. In a samp

le of 100 items, 55 are defective. The lower bound of a 99% confidence interval for the proportion of defectives is ________.
Mathematics
1 answer:
fenix001 [56]2 years ago
6 0

Answer:

The lower bound of a 99% C.I for the proportion of defectives = 0.422

Step-by-step explanation:

From the given information:

The point estimate = sample proportion \hat p

\hat p = \dfrac{x}{n}

\hat p = \dfrac{55}{100}

\hat p = 0.55

At Confidence interval of 99%, the level of significance = 1 - 0.99

= 0.01

Z_{\alpha/2} =Z_{0.01/2} \\ \\ = Z_{0.005} = 2.576

Then the margin of error E = Z_{\alpha/2} \times \sqrt{\dfrac{\hat p(1-\hat p)}{n}}

E = 2.576 \times \sqrt{\dfrac{0.55(1-0.55)}{100}}

E = 2.576 \times \sqrt{\dfrac{0.2475}{100}}

E = 2.576 \times0.04975

E = 0.128156

E ≅ 0.128

At 99% C.I for the population proportion p is: \hat p - E

= 0.55 - 0.128

= 0.422

Thus, the lower bound of a 99% C.I for the proportion of defectives = 0.422

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nexus9112 [7]

Answer:

a) The sampling distirbution has a mean of 135 and a standard deviation of 1.732.

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Step-by-step explanation:

a) We are taking samples of size n=3, as we are taking 3 readings daily.

Each reading has a mean of 135 and a standard deviation of 3.

The sampling distribution depends on the population parameters and the sample size.

The mean of the sampling distribution is equal to the population mean. In this case, the mean of the sampling distribution is 135.

The standard deviation depends on the standard deviation of the population and the sample size, and is calculated as:

\sigma_M=\dfrac{\sigma}{\sqrt{N}}=\dfrac{3}{\sqrt{3}}=1.732

b) The sampling distribution is also bell shaped, centered in the population mean. It has less spread that the population distribution because the standard deviation is smaller.

c) The probability that the sample mean exceeds 140 can be calculated using the standard normal distribution.

First, we have to calculate the z-score for X=140. We use for this the mean and standard deviation of the sampling distribution.

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With this z-score, we can look up the probabilty in the standard normal distribution

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3 years ago
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Answer:

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