1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Elanso [62]
3 years ago
11

Do political science classes require less writing than history classes? The 55 randomly selected political science classes assig

ned an average of 19.6 pages of essay writing for the course. The standard deviation for these 55 classes was 4.8 pages. The 50 randomly selected history classes assigned an average of 20.2 pages of essay writing for the course. The standard deviation for these 50 classes was 3.3 pages. What can be concluded at the α α = 0.01 level of significance?
Mathematics
1 answer:
tia_tia [17]3 years ago
8 0

Answer:

No, political science classes does not require less writing than history classes.

Step-by-step explanation:

We are given that the 55 randomly selected political science classes assigned an average of 19.6 pages of essay writing for the course. The standard deviation for these 55 classes was 4.8 pages.

The 50 randomly selected history classes assigned an average of 20.2 pages of essay writing for the course. The standard deviation for these 50 classes was 3.3 pages.

<em>Let </em>\mu_1<em> = mean writing required by political science classes</em>

<em />\mu_2<em> = mean writing required by history classes</em>

SO, Null Hypothesis, H_0 : \mu_1-\mu_2\geq0  or  \mu_1\geq \mu_2    {means that political science classes require more or equal writing than history classes}

Alternate Hypothesis, H_A : \mu_1-\mu_2  or  \mu_1   {means that political science classes require less writing than history classes}

The test statistics that will be used here is <u>Two-sample t test statistics</u> as we don't know about the population standard deviations;

                     T.S.  = \frac{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)}{s_p\sqrt{\frac{1}{n_1}+\frac{1}{n_2}  } }  ~ t__n__1+_n__2-2

where, \bar X_1 = sample average writing for political science course= 19.6 pages

\bar X_2 = sample average writing for history course= 20.2 pages

s_1 = sample standard deviation for political science classes = 4.8 pages

s_2 = sample standard deviation for history classes = 3.3 pages

n_1 = sample of selected political science classes = 55

n_2 = sample of selected history classes = 50

Also, s_p=\sqrt{\frac{(n_1-1)s_1^{2}+(n_2-1)s_2^{2}  }{n_1+n_2-2} }  =  \sqrt{\frac{(55-1)\times 4.8^{2}+(50-1)\times 3.3^{2}  }{55+50-2} }  = 4.154

So, <u><em>the test statistics</em></u>  =  \frac{(19.6-20.2)-(0)}{4.154 \times \sqrt{\frac{1}{55}+\frac{1}{50}  } }  ~  t_1_0_3

                                     =  -0.739

<em>Now at 0.01 significance level, the t table gives critical value of -2.367 at 103 degree of freedom for left-tailed test. Since our test statistics is more than the critical value of t as -0.739 > -2.367, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.</em>

Therefore, we conclude that political science classes require more or equal writing than history classes.

You might be interested in
Question a) Compare the Variability of Expenditure of Families in Two Towns given as follows: Number of families Expenditure (Ru
Karolina [17]

Answer:

Kindly check explanation

Step-by-step explanation:

Given the data:

Number of families __________Expenditure

______midpoint (x) ____Town A __Town B

21-30 __25.5____________3 _______2

31-40 __35.5____________61 ______14

41-50 __45.5___________132 _____ 20

51-60 __55.5__________ 153 ______27

61-70 __65.5__________ 140 ______ 28

71-80 __75.5___________ 51 _______ 7

81-90 __85.5___________ 2 _______ 2

The variability is the variance and standard deviation :

The variance (s):

√Σ(x - m)²/Σf(x)

Town A:

m = Σ(X * f(x)) / Σf ; Σf = 542

Σ x * f(x) = (25.5*3) + (35.5*61) + (45.5*132) + (55.5*153) + (65.5*140) + (75.5*51) + (85.5*2)

= 29931 / 542

= 55. 22

Σf(x - m)² / Σf - 1 = [3(25.5-55.22)^2 + 61(35.5-55.22)^2 + 132(45.5-55.22)^2 + 153(55.5-55.22)^2 + 140(65.5-55.22)^2 + 51(75.5-55.22)^2 + 2(85.5-55.22)^2] / 541

= 76458. 4928 / 541

Variance = 141.32808

Standard deviation = √variance

Standard deviation = √141.32808

Standard deviation = 11.89

TOWN B:

m = Σ(X * f(x)) / Σf ; Σf = 100

Σ x * f(x) = (25.5*2) + (35.5*14) + (45.5*20) + (55.5*27) + (65.5*28) + (75.5*7) + (85.5*2)

= 5490 / 100

= 54.90

Variance :

Σf(x - m)² / Σf - 1 = [2(25.5-54.90)^2 + 14(35.5-54.90)^2 + 20(45.5-54.90)^2 + 27(55.5-54.90)^2 + 28(65.5-54.90)^2 + 7(75.5-54.90)^2 + 2(85.5-54.90)^2] / 99

= 16764 / 99

= 169.33

Standard deviation = √variance

Standard deviation = √169.3333

Standard deviation = 13.013

From the result above, Town A has lesser variability than Town B due to the slightly lower variance and standard deviation values.

8 0
3 years ago
PLEASE HELP ME NOW! THIS IS DUE AND I NEED HELP, please and thank you.
GaryK [48]
Hfdjuggb 77₽+I /2-1₽5
3 0
2 years ago
Suppose you want to fence in some land along the edge of a straight river. the fenced area will be in the shape of a rectangle,
m_a_m_a [10]
For the largest area, half the fence is used parallel to the river, and the other half is used for the two ends of the rectangular space.

The dimensions are 475 m by 237.5 m.

_____
Let x represent the length along the river. Then the area (A) is found as
.. A = x*(950 -x)/2
This equation describes a parabola with its vertex (maximum) halfway between the zeros of x=0 and x=950. That is, the maximum area is achieved when half the fence is used parallel to the river.

7 0
3 years ago
True or false? Postulates are statements that are accepted without question or justification
ale4655 [162]
<span>True, as a postulate is the assumption of existence.</span>
6 0
3 years ago
Read 2 more answers
Please help with 5 I don’t get it
Alexxandr [17]

Answer:

It’s saying for every 1/4 inch, you have 3 feet. Let’s say I had an inch. That means I have 12 feet. Hope this helped!

Step-by-step explanation:

I only have an explanation. I don’t have the answer, but maybe I could help!

3 0
3 years ago
Other questions:
  • If you get this right I will mark you as a brainliest
    7·2 answers
  • Find the product 12, -5 (a) -60 (b) 17 (c) 7 (d) -2.4
    15·1 answer
  • Joe borrowed 2000$ from a bank at a rate of 7% simple interest per year how much interest did he pay in 5 years?
    15·1 answer
  • Round 653,500 to the nearest thousand
    14·2 answers
  • You put a border around the perimeter of this room. How many yards of border did you
    5·1 answer
  • If sin⁡ θ=− 8/17 and 270°&lt;θ&lt;360°, what is cos⁡ θ?
    6·1 answer
  • Solve for x using the correct order operations
    9·1 answer
  • The temperature was 48°F and dropped 15° in two hours.
    12·2 answers
  • What is the value of x? ill give brainliest!
    15·2 answers
  • ALL MY POINTS!! ANSWER NOW PLEASEEE
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!