Where is the blue dot located

A school authority claims that the average height of students is 178 cm. A researcher has taken a well-designed survey and his s

Hunter-Best [27]

Answer:

d) The difference exists due to chance since the test statistic is small

Step-by-step explanation:

From the given information:

Population mean = 178 cm

the sample mean = 177.5 cm

the standard deviation = 2

the sample size = 25

The null hypothesis and the alternative hypothesis can be computed as:

Null hypothesis:

$H_o: \mu = 178$

Alternative hypothesis:

$H_1: \mu \neq 178$

The t-test statistics is determined by using the formula:

$t = \dfrac{X - \mu}{\dfrac{\sigma}{\sqrt{n}}}$

$t = \dfrac{177.5 - 178}{\dfrac{2}{\sqrt{25}}}$

$t = \dfrac{-0.5}{\dfrac{2}{5}}}$

$\mathbf{t= -1.25}$

Degree of freedom df = n- 1

Degree of freedom df = 25 - 1

Degree of freedom df = 24

At the level of significance ∝ = 0.05, the critical value = 2.064

Decision rule: To reject the null hypothesis if the test statistics is greater than the critical value at 0.05 level of significance

Conclusion: We fail to reject the null hypothesis since the test statistics is lesser than the critical value and we conclude that the difference exists due to chance since the test statistic is small

5 0

2 years ago

A scientist is studying the motion of waves by measuring the distance between the crests and troughs of waves in a particular ar

Vikentia [17]

Answer:

this is correct on plato/edmentum

Step-by-step explanation:

3 0

2 years ago

Please help me solve these problems

vovangra [49]

Will do first question of each concept only because the rest of the questions are the same concept (the same few repeat but whatever).

1. Total angle = (n - 2) * 180 --> 4 * 180 = 360°

70 + 130 + 120 + θ = 360 --> 320 + θ = 360 --> θ = 40

4. Total angle = (10 - 2) * 180 --> 8 * 180 = 1440

1440/10 = 144°

6. Interior: (n - 2) * 180 --> 10 * 180 = 1800

Exterior: 12 * 180 = 2160 --> 2160 - 1800 = 360

9. (n - 2) * 180 --> 3 * 180 = 540

90 + 90 + 150 + 160 + θ = 540 --> 490 + θ = 540 --> θ = 50

13. Interior: (n - 2) * 180 --> 2 * 180 = 360

Exterior: n * 180 - (n - 2) * 180 --> 180n - 180n + 360 --> 360 (always the same)

16. 7r + 4r + 8r + 5r = 360 --> 24r = 360 --> r = 15

5 0

3 years ago

Plzzzzzzzzz answer fast brainlist and five stars

Kruka [31]

Answer:

C

Step-by-step explanation:

trust

3 0

3 years ago

A restaurant sells about 330 sandwiches each day at a price of $6 each $.25 decrease in price. 15 more sandwiches are sold per d

zmey [24]

Answer:

restaurant should charge $(6-0.25) = $5.75per sandwich to maximize daily revenue.

the revenue is $1983.75

Step-by-step explanation:

to calculate current revenue= $6 x 330 = $1980

suppose x as the number of times the price to be dropped by $0.25

then find new price.. i.e

new price= $(6-0.25x)

and, new sell=330 +15x sandwiches

therefore, the new revenue would be= (6-0.25x)(330 +15x)

in order to maximize the current revenue, simplify the above equation and make it complete square using x

(6-0.25x)(330 +15x)

=1980-82.5x +90x -3.75 $x^{2}$

=1980 + 7.5x -3.75 $x^{2}$

=1980-3.75 (-2x+ $x^{2}$ ) ----> taking out common

now, to make a complete square lets add and subtract 1 inside the parentheses

=1980-3.75(-1+1-2x+ $x^{2}$ )

=1980 +3.75 -3.75( $x^{2}$ -2x +1)

=1983.75 -3.75 $(x-1)^{2}$ ---->(1)

as $(x-1)^{2}$ is positive always, minimize the other term in order to maximize the total revenue.

so the minimum possible value of $(x-1)^{2}$ = 0

therefore, x=1

putting x in eq(1) the revenure becomes,

$(1983.75-0)=> $1983.75

therefore, restaurant should charge $(6-0.25) = $5.75per sandwich to maximize daily revenue.

the revenue is $1983.75

3 0

3 years ago