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Rina8888 [55]
3 years ago
5

Last school year, the student body of a local university consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors

. A sample of 300 students taken from this year's student body showed the following number of students in each classification.
Freshmen 83
Sophomores 68
Juniors 85
Seniors 64
We are interested in determining whether or not there has been a significant change in the classifications between the last school year and this school year.

Mathematics
1 answer:
Natalija [7]3 years ago
6 0

Answer:

There has been no change in the classifications between the last school year and this school year.

Step-by-step explanation:

A Chi-square test for goodness of fit will be used in this case.

The hypothesis can be defined as:

<em>H</em>₀: The observed frequencies are same as the expected frequencies.

<em>Hₐ</em>: The observed frequencies are not same as the expected frequencies.

The test statistic is given as follows:

\chi^{2}=\sum\limits^{n}_{i=1}\frac{(O_{i}-E_{i})^{2}}{E_{i}}

The expected values are computed using the formula:

E_{i}=p_{i}\times N

Here, <em>N</em> = 300

Use Excel to compute the values.

The test statistic value is:

\chi^{2}=\sum\limits^{n}_{i=1}\frac{(O_{i}-E_{i})^{2}}{E_{i}}=1.662

The test statistic value is, 1.662.

The degrees of freedom of the test is:

<em>n</em> - 1 = 4 - 1 = 3

The significance level is, <em>α</em> = 0.05.

Compute the p-value of the test as follows:

<em>p</em>-value = 0.6454

*Use a Chi-square table.

p-value = 0.6454 > <em>α</em> = 0.05.

So, the null hypothesis will not be rejected at 5% significance level.

Thus, concluding that there has been no change in the classifications between the last school year and this school year.

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Find the area and the perimeter of the shaded region
lyudmila [28]

Answer:

area: 41.04 cm² ; perimeter 35.8 cm

Step-by-step explanation:

Perimeter of shaded area = 1/4 perimeter of circle + line AC = ¼ * 3.14 * 2 * 12 + √(12² + 12²) = 18.84 + 12√2 cm = 35.8 cm

Area of Shaded Region = 1/4 area of circle - area of triangle = ¼ * 3.14 * 12² - ½ . 12 * 12

= (¼ * 3.14 - ½) * 12² = 41.04 cm²

8 0
3 years ago
What is the measure of ∠L?
otez555 [7]
<h3>Answer:  72.54</h3>

====================================================

Explanation:

We set up a cosine ratio, since we want to connect the adjacent and hypotenuse. Then we'll use the inverse cosine, which is also known as arccosine, to isolate the angle value.

This is what your steps could look like:

cos(angle) = adjacent/hypotenuse

cos(L) = LM/LN

cos(L) = 18/60

cos(L) = 0.3

L = arccos(0.3)

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L = 72.54 degrees approximately

Make sure your calculator is in degree mode.

8 0
2 years ago
7 - 5n = 6 + 6(n + 2)
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