© A, B and C form a triangle where ZBAC = 90°.

How to calculate standard deviation sample?

Harman [31]

Formula for standard deviation sample calculation is:
SD = sqrt (( ∑( x - m)²) / ( n - 1 )),
where x stays for each value in the data set, m stays for mean of all values in the data set, and n stays for the number of values in the data set.
For example: Find the sample standard deviation for the set of numbers: 10, 11, 11, 12, 12.
First we will find mean of all avlues: m = ( 10 + 11 + 11 + 12 +12 ) / 5 = 11.2
SD = sqrt (( 1.2² + 0.2² + 0.2² + 0.8² + 0.8² ) / ( 5 - 1 ))=
= sqrt ( 2.8 / 4 ) = √0.7 = 0.837

7 0

4 years ago

A study is done to determine if students in the California state university system (sample 1) take longer to graduate, on averag

Debora [2.8K]

Answer:

We conclude that the students in the California state university system take longer to graduate as compared to students enrolled in private universities.

Step-by-step explanation:

We are given that from years of research, it is known that the population standard deviations are 1.5 years and 0.9 years, respectively.

One hundred students from each the California state university system and private universities are surveyed. The California state university system students took on average 4.8 years while the private university students took on average 4.4 years.

Let $\mu_1$ = population average time taken by students in the California state university system to graduate

$\mu_2$ = population average time taken by students in the private universities to graduate

SO, Null Hypothesis, $H_0$ : $\mu_1-\mu_2\leq0$ or $\mu_1 \leq \mu_2$ {means that the students in the California state university system take less than or equal time to graduate as compared to students enrolled in private universities}

Alternate Hypothesis, $H_A$ : $\mu_1-\mu_2 >0$ or $\mu_1>\mu_2$ {means that the students in the California state university system take longer to graduate as compared to students enrolled in private universities}

The test statistics that will be used here is Two-sample z test statistics as we know about the population standard deviations;

T.S. = $\frac{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)}{\sqrt{\frac{\sigma_1^{2} }{n_1} + \frac{\sigma_2^{2} }{n_2}} }$ ~ N(0,1)

where, $\bar X_1$ = sample average time taken by the California state university system students to graduate = 4.8 years

$\bar X_2$ = sample average time taken by the private university students to graduate = 4.4 years

$\sigma_1$ = population standard deviation for California state university system students = 1.5 years

$\sigma_2$ = population standard deviation for private university students = 0.9 years

$n_1$ = sample of California state university system students taken = 100

$n_2$ = sample of private university students taken = 100

So, test statistics = $\frac{(4.8-4.4)-(0)}{\sqrt{\frac{1.5^{2} }{100} + \frac{0.9^{2} }{100}} }$

= 2.287

Now at 0.10 significance level, the z table gives critical value of 1.2816 for right-tailed test. Since our test statistics is more than the critical value of z so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.

Therefore, we conclude that the students in the California state university system take longer to graduate as compared to students enrolled in private universities.

5 0

4 years ago

Help ! With step by step solution

nirvana33 [79]

Answer:

the correct answer is C

Step-by-step explanation:

first step you change the x and y powers to the square root(showing in the pic).

second the number outside of the parenthesis times the numbers inside the parenthesis and then you just figure it out how it works...

7 0

3 years ago

A segment of length 94 cm has been rotated d degrees around a center 0. What is the length of the rotated segment? How do you kn

Gekata [30.6K]

Answer:

Length of rotated segment = 94 cm

Step-by-step explanation:

Rotation is transformation of a figure or a segment about a center which rotates the figure or segment about the center with the angle of rotation.

Rotation is that type of transformation in which the image and pre-image are congruent. This means that rotation has no effect on shape and size of figure or segment and thus, the shape and size of the figure or segment remains same after rotation.

It is given that a segment of length 94 cm is rotated $d$ degrees around a center $O$ .

The rotation will have no effect on size of the segment as stated above.

Thus, the segment after rotation will still measure 94 cm.

8 0

4 years ago

The cost of admission to a history museum is $3.25 per person over the age of three , kids three and under get in for free. If t

svetlana [45]

19.50 divided by 3.25 is 6
6 family members in total.

6 0

4 years ago