24/52 simplify fraction

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

saul85 [17]

Answer:

We conclude that political science classes require less writing time than history classes at 0.01 level of significance.

Step-by-step explanation:

We are given that the 55 randomly selected political science classes assigned an average of 16.3 pages of essay writing for the course. The standard deviation for these 55 classes was 4.8 pages.

The 54 randomly selected history classes assigned an average of 18.9 pages of essay writing for the course. The standard deviation for these 54 classes was 5 pages.

Let $\mu_1$ = average writing time required by political science classes.

$\mu_2$ = average writing time required by history classes.

So, Null Hypothesis, $H_0$ : $\mu_1\geq\mu_2$ {means that political science classes require more or equal writing time than history classes}

Alternate Hypothesis, $H_A$ : $\mu_1$ {means that political science classes require less writing time than history classes}

The test statistics that would be used here Two-sample t test statistics as we don't know about the population standard deviation;

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 pages of essay writing for political science classes = 16.3 pages

$\bar X_2$ = sample average pages of essay writing for history classes = 18.9 pages

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

$s_2$ = sample standard deviation for history classes = 5 pages

$n_1$ = sample of political science classes = 55

$n_2$ = sample of history classes = 54

Also, $s_p=\sqrt{\frac{(n_1-1)s_1^{2}+(n_2-1)s_2^{2} }{n_1+n_2-2} }$ = $\sqrt{\frac{(55-1)\times 4.8^{2}+(54-1)\times 5^{2} }{55+54-2} }$ = 4.90

So, test statistics = $\frac{(16.3-18.9)-(0)}{4.9 \sqrt{\frac{1}{55}+\frac{1}{54} } }$ ~ $t_1_0_7$

= -2.77

The value of t test statistics is -2.77.

Now, at 0.01 significance level the t table gives critical value of -2.365 at 107 degree of freedom for left-tailed test.

Since our test statistics is less than the critical value of t, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that political science classes require less writing time than history classes.

3 0

3 years ago

First right answer gets brain

Maurinko [17]

It is a ray. Which is a... please thank me

6 0

3 years ago

Adjust the number into correct standard form. 96 × 10^−2

SSSSS [86.1K]

Answer:

Since the exponent of the scientific notation is negative, move the decimal point 2 places to the left.

0.96

8 0

3 years ago

What is the equivalent of 3/8

mixas84 [53]

Answer:

6/16 is equivalent to 3/8 because after dividing the numerator (6) and denominator (16) we get 3/8.

8 0

3 years ago

Read 2 more answers

a half cup of pancakes mix has 5% total daily allowance of cholesterol. the total daily allowance of cholesterol 300 mg. how muc

arsen [322]

Hi there!

Since we know that the pancake mix has 5% of the daily allowance, which is 300 mg, we can just multiply 300 mg with 5 percent to get our answer.

First, let's divide 5% by 100% to know what we are going to multiply 300 mg with.

5% / 100% = 0.05

Let's multiply 300 mg with 0.05

0.05 * 300 = 15 mg

Thus, a 1/2 cup of pancake mix has 15 mg of cholesterol.

Have an awesome day! :)

6 0

3 years ago