Mathematics, 23.04.2020 03:07, eto911

A 99% confidence interval (in inches) for the mean height of a population is 65.67 < μ < 67.13. This result is based on a sample of size 144. If the confidence interval 65.87 < μ < 66.93 is obtained from the same sample data, what is the degree of confidence?

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answered: karlacr5117

Confidence = 0.94 = 94%

Step-by-step explanation:

Solution:-

- A 99% confidence interval (in inches) for the mean height of a population is:

65.44 < μ < 66.96

- If the confidence interval is obtained from the same sample data:

65.65 < μ < 66.75

- The sample size, n = 144

- You will first need to find the sample mean (x_bar) and sample standard deviation (s) based on the confidence interval given. The width of the confidence interval is 2E

2E = 66.96-65.44 = 1.52

E = 0.76

- The test statistic error (E) is defined as:

$E = z-critical*\frac{s}{\sqrt{n} }$

Where, Z-critical for 99% confidence = 2.5758

$s = E*\frac{\sqrt{n} }{z-critical} \\\\s = 0.76*\frac{\sqrt{144} }{2.5758}\\\\s=3.54$

- Since,

x_bar - E = 65.44

x_bar = 65.44 - 0.76 = 66.2

- Use the value you found in part a to determine the degree of confidence for the interval 65.65 < μ < 66.75 is based on:

66.2 - E = 65.65

E = 0.55

- The test statistic error (E) is defined as:

$E = z-critical*\frac{s}{\sqrt{n} }$

- Determine the Z-critical value from equation above:

$z-critical = E*\frac{\sqrt{n} }{s} \\\\z-critical = 0.55*\frac{\sqrt{144} }{3.54}\\\\z-critical=1.864$

- The level of confidence for the corresponding Z-critical value would be:

Confidence = P ( - z-critical < Z < z-critical )

Confidence = P ( - 1.864 < Z < 1.864 )

Confidence = 0.94 = 94%

answered: Guest

fabric (square meters) cloaks

7 21

4/3 4

step-by-step explanation:

we are told that harry needs 2 square meters of fabric for every 6 wizard cloaks he makes.

1. first of all we will find how many cloaks can be made from 1 square meter of fabric by dividing 6 by 2.

we can see that 3 cloaks can be made from 1 square meter of fabric. now we will multiply 3 by 7 to find number of cloaks made from 7 square meters of fabric.

therefore, harry will make 21 cloaks from 7 square meters of fabric.

2. let us find how many square meters of fabric will be needed to make 4 cloaks.

first of all we will find fabric needed for 1 cloak by dividing 2 by 6.

we can see that fabric needed for 1 cloak is square meter. now we will multiply by 4 to find fabric needed for 4 cloaks.

answered: Guest

i don't know i don't know