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2 years ago

Evaluate 4b-3c-7 for b=4 and c=1

Mathematics

2 answers:

coldgirl [10]2 years ago

5 0

Plug in 4 for b and 1 for c.

4*4 - 3*1 - 7 = 6

Alex2 years ago

4 0

The answer is 8

Happy studying!

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Information about the proportion of a sample that agrees with a certain statement is given below. Use StatKey or other technolog

lara31 [8.8K]

Answer:

$SE=\sqrt{\frac{\hat p (1-\hat p)}{n}}=\sqrt{\frac{0.35 (1-0.35)}{100}}=0.048$

If we replace the values obtained we got:

$0.35 - 1.96\sqrt{\frac{0.35(1-0.35)}{100}}=0.257$

$0.42 + 1.96\sqrt{\frac{0.42(1-0.42)}{150}}=0.443$

The 95% confidence interval would be given by (0.257;0.443)

Step-by-step explanation:

Notation and definitions

$X=35$ number of people that agree.

$n=100$ random sample taken

$\hat p=\frac{35}{100}=0.35$ estimated proportion of people that agree

$p$ true population proportion of peopl that agree

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by:

$z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96$

The confidence interval for the mean is given by the following formula:

$\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$

The standard error is given by:

$SE=\sqrt{\frac{\hat p (1-\hat p)}{n}}=\sqrt{\frac{0.35 (1-0.35)}{100}}=0.048$

If we replace the values obtained we got:

$0.35 - 1.96\sqrt{\frac{0.35(1-0.35)}{100}}=0.257$

$0.42 + 1.96\sqrt{\frac{0.42(1-0.42)}{150}}=0.443$

The 95% confidence interval would be given by (0.257;0.443)

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Three students want to estimate the mean word length of the same book. To do this, each student randomly chose 4 words from the

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The solutions to the questions are given below

sample(n) word length sample mean

1 5,4,4,2 3.75

2 3,2,3,6 3.5

3 5,6,3,3 4.25

b)R =0.75

The mean of the sample means will tend to be a better estimate than a single sample mean.
The closer the range of the sample means is to 0, the more confident they can be in their estimate.

<h3>What is the students are going to use the sample means to estimate the mean word length in the book.?</h3>

The table below shows sample means in the table.

sample(n) word length sample mean

1 5,4,4,2 3.75

2 3,2,3,6 3.5

3 5,6,3,3 4.25

Generally, the equation for is mathematically given as

variation in the sample means

R =maximum -minimum

R=4.25-3.5

R =0.75

In conclusion, In most cases, the mean of many samples will provide a more accurate estimate than the mean of a single sample.

They may have a higher level of confidence in their estimate if the range of the sample means is closer to 0 than it is now.