Answer:
The sample consisting of 64 data values would give a greater precision.
Step-by-step explanation:
The width of a (1 - <em>α</em>)% confidence interval for population mean μ is:
So, from the formula of the width of the interval it is clear that the width is inversely proportion to the sample size (<em>n</em>).
That is, as the sample size increases the interval width would decrease and as the sample size decreases the interval width would increase.
Here it is provided that two different samples will be taken from the same population of test scores and a 95% confidence interval will be constructed for each sample to estimate the population mean.
The two sample sizes are:
<em>n</em>₁ = 25
<em>n</em>₂ = 64
The 95% confidence interval constructed using the sample of 64 values will have a smaller width than the the one constructed using the sample of 25 values.
Width for n = 25:
![\text{Width}=2\cdot z_{\alpha/2}\cdot \frac{\sigma}{\sqrt{25}}=\frac{1}{5}\cdot [2\cdot z_{\alpha/2}\cdot \sigma]](https://tex.z-dn.net/?f=%5Ctext%7BWidth%7D%3D2%5Ccdot%20z_%7B%5Calpha%2F2%7D%5Ccdot%20%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7B25%7D%7D%3D%5Cfrac%7B1%7D%7B5%7D%5Ccdot%20%5B2%5Ccdot%20z_%7B%5Calpha%2F2%7D%5Ccdot%20%5Csigma%5D)
Width for n = 64:
![\text{Width}=2\cdot z_{\alpha/2}\cdot \frac{\sigma}{\sqrt{64}}=\frac{1}{8}\cdot [2\cdot z_{\alpha/2}\cdot \sigma]](https://tex.z-dn.net/?f=%5Ctext%7BWidth%7D%3D2%5Ccdot%20z_%7B%5Calpha%2F2%7D%5Ccdot%20%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7B64%7D%7D%3D%5Cfrac%7B1%7D%7B8%7D%5Ccdot%20%5B2%5Ccdot%20z_%7B%5Calpha%2F2%7D%5Ccdot%20%5Csigma%5D)
Thus, the sample consisting of 64 data values would give a greater precision
Given:
Elliot has a total of 26 books. He has 12 more fiction books than nonfiction books.
To Find:
A system of linear equations represents the situation.
Answer:
Step-by-step explanation:
We are given that x represents the number of fiction books and y is the number of non-fiction books.
We are also given that the total number of books Elliot has is 26 which includes both fiction and non-fiction. So, we may write
Next, we are given that there are 12 more fiction books than non-fiction books. This means, the fiction books are more in number and so, we may write
So, the total system of equations can be represented as
Answer:7
Step-by-step explanation:
This can be solved by Venn-diagram
Given there are total 5 students who want french and Latin
also 3 among them want Spanish,french & Latin
i.e. only 2 students wants both french and Latin only.
Also Student who want only Latin is 5
Thus Student who wants Latin and Spanish both only is 11-5-3-2=1
Students who want only Spanish is 8 Thus students who wants Spanish and French is 4
Similarly Students who wants Only French is 16-4-3-2=7
<u>Answer:</u>
If PQ=RS then PQ and RS have the same length. Hence option D is correct
<u>Solution:</u>
Given that, pq = rs
And, we have to find which of the given options are true.
<u><em>a) pq and rs form a straight angle
</em></u>
We can’t decide the angle in between pq and rs just by the statement pq = rs.
So this statement is false.
<u><em>b) pq and rs form a zero angle.
</em></u>
We can’t decide the angle in between pq and rs just by the statement pq = rs.
So this statement is false.
<u><em>c) pq and rs are same segment.
</em></u>
If two things equal then there is no condition that both represents a single item.
So this statement is false.
<u><em>d) pq and rs have the same length
</em></u>
As given that pq = rs, we can say that they will have the same length
Hence, option d is true.
Answer:
4585.8 feet
Step-by-step explanation:
If we draw the triangle, the opposite side to 3° angle would be "10" less than total height of 250 because Nick is 10 feet above water level, so that side will be:
250 - 10 = 240
The hypotenuse of the triangle is the length of line of sight. We can call this "x".
So, using trigonometric ratio of sine (opposite/hypotenuse), we can write:
Now, we cross multiply and solve for x, line of sight length:
