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vovangra [49]
1 year ago
9

Find the 95% confidence interval for estimating the population mean μ

Mathematics
1 answer:
AVprozaik [17]1 year ago
8 0

We first need to determine whether we are dealing with means or proportions in this problem. Since we are given the sample and population mean, we know that we are dealing with means.

Since we have one sample mean, this means we are creating a confidence interval for one sample (1 Samp T Int).

Normally we would check for conditions, but since this is not formulated as a "real-world scenario" type problem, it is hard to check for randomness and independence. Therefore, I will be excluding conditions from this answer.

<h3>Confidence Interval Formula</h3>

The formula for constructing a <u>confidence interval for means</u> is as follows:

  • \displaystyle \overline{x} \pm t^*\big{(}\frac{\sigma}{\sqrt{n} } \big{)}

We are given these variables:

  • \overline{x}=50
  • n=60
  • \sigma=10

Plug these values into the formula for the confidence interval:

  • \displaystyle 50\pm t^* \big{(}\frac{10}{\sqrt{60} } \big{)}

<h3>Finding the Critical Value (t*)</h3>

In order to find t*, we can use this formula:

  • \displaystyle \frac{1-C}{2}=A

Calculating the z-score associated with "A" will give us t*.

So, let's plug in the confidence interval 95% (.95) into the formula:

  • \displaystyle \frac{1-.95}{2}=.025

Use your calculator or a t-table to find the z-score associated with this area under the curve.. you should get:

  • t^*=1.96

<h3>Constructing Confidence Interval</h3>

Now, let's finish the confidence interval we created:

  • \displaystyle 50\pm 1.96 \big{(}\frac{10}{\sqrt{60} } \big{)}

We can calculate the confidence interval, using this formula, to be:

  • \boxed{(47.4697, \ 52.5303)}

<h3>Interpreting the Confidence Interval</h3>

We are 95% confident that the true population mean μ lies between <u>47.4697 and 52.5303</u>.

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3 years ago
Bradley estimated the height of a tree at 2.5 meters. Carla estimated that tree's height at 8 feet.
vredina [299]

Answer: 4.1 feet : 4 feet

Step-by-step explanation:

From the question, we are informed that Bradley estimated the height of a tree at 2.5 meters. Carla estimated that tree's height at 8 feet.

The conversion ratio be used to compare Bradley's and Carla's estimates of the tree's height when measured in feet goes thus:

Since 1 feet = 0.305 meters

2.5 meters will be = 2.5/0.305 = 8.2 feet

Therefore the conversion ratio will be:.

= 8.2 : 8

Reducing to lowest term will be

= 4.1 feet : 4 feet.

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Assuming that the sample mean carapace length is greater than 3.39 inches, what is the probability that the sample mean carapace
joja [24]

Answer:

The answer is "".

Step-by-step explanation:

Please find the complete question in the attached file.

We select a sample size n from the confidence interval with the mean \muand default \sigma, then the mean take seriously given as the straight line with a z score given by the confidence interval

\mu=3.87\\\\\sigma=2.01\\\\n=110\\\\

Using formula:

z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}  

The probability that perhaps the mean shells length of the sample is over 4.03 pounds is

P(X>4.03)=P(z>\frac{4.03-3.87}{\frac{2.01}{\sqrt{110}}})=P(z>0.8349)

Now, we utilize z to get the likelihood, and we use the Excel function for a more exact distribution

=\textup{NORM.S.DIST(0.8349,TRUE)}\\\\P(z

the required probability: P(z>0.8349)=1-P(z

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2 years ago
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elixir [45]

Answer:

A

Step-by-step explanation:

m - 11 = 43

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Write an algebraic expression for the phrase. 5 times the sum of p and r
DedPeter [7]
The correct answer is 5(p+r) because sum means add

Hope this helped :)
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