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podryga [215]
4 years ago
8

Assume that a sample is used to estimate a population proportion p. Find the 99% confidence interval for a sample of size 133 wi

th 61.7% successes. Enter your answer as an open-interval (i.e., parentheses) using decimals (not percents) accurate to three decimal places.
Mathematics
1 answer:
RideAnS [48]4 years ago
8 0

Answer:

The 99% confidence interval is (0.508, 0.726).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

z is the zscore that has a pvalue of 1 - \frac{\alpha}{2}.

For this problem, we have that:

n = 133, p = 0.617

99% confidence level

So \alpha = 0.01, z is the value of Z that has a pvalue of 1 - \frac{0.01}{2} = 0.995, so Z = 2.575.

The lower limit of this interval is:

\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.617 - 2.575\sqrt{\frac{0.617*0.383}{133}} = 0.508

The upper limit of this interval is:

\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.617 + 2.575\sqrt{\frac{0.617*0.383}{133}} = 0.726

The 99% confidence interval is (0.508, 0.726).

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Green Frog convenience store supplies two types of protein bars. One protein bar has 320 calories in the 2-ounce size. How many
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Answer:

I think it is C) 480

Step-by-step explanation:

320÷2=160

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<em>Can I please have Brainliest? </em>

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3 years ago
What is the recursive formula of the arithmetic sequence 4,22,40,58
TiliK225 [7]

Hello from MrBillDoesMath!

Answer:

T(1) = 4

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Discussion:

Consecutive terms appear to increase by 18. This suggests the formula

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8 0
3 years ago
Read 2 more answers
A manufacturer makes chocolate squares that have a target weight of 8 g. Quality control engineers sample 30 chocolate squares t
posledela

Using the <em>normal distribution and the central limit theorem</em>, it is found that the power of the test is of 0.9992 = 99.92%.

<h3>Normal Probability Distribution</h3>

In a normal distribution with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

  • It measures how many standard deviations the measure is from the mean.
  • After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.
  • By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation s = \frac{\sigma}{\sqrt{n}}.

In this problem:

  • The mean is \mu = 8.5.
  • The standard deviation is \sigma = 0.87.
  • A sample of 30 is taken, hence n = 30, s = \frac{0.87}{\sqrt{30}} = 0.1588.

The power of the test is given by the probability of a sample mean above 8, which is <u>1 subtracted by the p-value of Z when X = 8</u>, so:

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem:

Z = \frac{X - \mu}{s}

Z = \frac{8 - 8.5}{0.1588}

Z = -3.15

Z = -3.15 has a p-value of 0.0008.

1 - 0.0008 = 0.9992.

The power of the test is of 0.9992 = 99.92%.

To learn more about the <em>normal distribution and the central limit theorem</em>, you can check brainly.com/question/24663213

5 0
3 years ago
What is the equation of the line described below written in slope-intercept form?
mihalych1998 [28]

Answer:

D

Step-by-step explanation:

eq. of given line is x+y=10

eq. of any line parallel to given line is x+y=a

if it passes through (-1,5) then -1+5=a

or a=4

reqd. eq of line is x+y=4

or y=-x+4

5 0
4 years ago
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