20 people show up to a post-PSTAT 120A party. If everyone shakes hands with everyone else, how many handshakes take place

A random sample of 150recent donations at a certain

gtnhenbr [62]

Answer:

Null hypothesis: $p\geq 0.4$

Alternative hypothesis: $p < 0.4$

$z=\frac{0.3 -0.4}{\sqrt{\frac{0.4(1-0.4)}{150}}}=-2.5$

$p_v =2*P(Z$

If we compare the p value obtained and the significance level given $\alpha=0.01$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that the true proportion is not significantly lower than 0.4 or 40% at 1% of significance.

Step-by-step explanation:

1) Data given and notation

n=150 represent the random sample taken

X=45 represent the people with type A blood

$\hat p=\frac{45}{150}=0.3$ estimated proportion of people with type A blood

$p_o=0.4$ is the value that we want to test

$\alpha=0.01$ represent the significance level

Confidence=99% or 0.99

z would represent the statistic (variable of interest)

$p_v$ represent the p value (variable of interest)

2) Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that the true proportion of people type A blood is less than 0.4:

Null hypothesis: $p\geq 0.4$

Alternative hypothesis: $p < 0.4$

When we conduct a proportion test we need to use the z statisitc, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value $p_o$ .

3) Calculate the statistic

Since we have all the info requires we can replace in formula (1) like this:

$z=\frac{0.3 -0.4}{\sqrt{\frac{0.4(1-0.4)}{150}}}=-2.5$

4) Statistical decision

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

The significance level provided $\alpha=0.01$ . The next step would be calculate the p value for this test.

Since is a bilateral test the p value would be:

$p_v =2*P(Z$

If we compare the p value obtained and the significance level given $\alpha=0.01$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that the true proportion is not significantly lower than 0.4 or 40% at 1% of significance.

7 0

3 years ago

Fifth grade

Kitty [74]

The fraction of the original mass that was lost in the second month is 1/12.

<h3>What is the fraction?</h3>

A fraction is a non-integer that is made up of numerators and denominators. An example of a fraction is 1/10.

Weight lost in the first month = 1/6 x 120 = 20kg

Weight lost in the second month = 1/10 x (120 - 20)

= 1/10 x 100 = 10kg

Fraction of the original mass that was lost in the second month : weight lost in the second month / total mass

10 kg / 120 = 1/12

To learn more about multiplication of fractions, please check: brainly.com/question/1114498

#SPJ1

6 0

2 years ago

PLZ HELP!!!!!!!!!!!!! WILL GIVE BRAINLIST IF CORRECT

kozerog [31]

Donut = $0.14 tax so $2.14 and tea = $0.07 tax so $1.07

7 0

3 years ago

HELPPPPPPPPP WITH THESE GRAPH! YOU'LL GET BRAINLIEST IF YOU'RE CORRECT! ALSO... THERE'S 20 POINTS!

lara [203]

<u>Given</u>:

Four coordinates lying on the 3rd quadrant of the Cartesian plane are as follows: $\:$

C' = (–6, –5)
D' = (–6, –3)
E' = (–4, –3)
F' = (–4, –5)

<u>Translation</u>:

Since you've been asked to translate the coordinates of the vertices 2 units right and 8 units up, you'll need to add 2 to its x-coordinate and 8 to its y-coordinate.

C'(–6, –5)

ㅤㅤ= C'(–6 + 2, –5 + 8)

ㅤㅤ= C'(–4, 3)

D'(–6, –3)

ㅤㅤ= D'(–6 + 2, –3 + 8)

ㅤㅤ= D'(–4, 5)

E'(–4, –3)

ㅤㅤ= E'(–4 + 2, –3 + 8)

ㅤㅤ= E'(–2, 5)

F'(–4, –5)

ㅤㅤ= F'(–4 + 2, –5 + 8)

ㅤㅤ= F'(–2, 3)

<u>Final </u><u>answer</u>:

C' = (–4, 3)
D' = (–4, 5)
E' = (–2, 5)
F' = (–2, 3)

4 0

3 years ago

Read 2 more answers

Three trigonometric functions for a given angle are shown below. Sine theta = Negative StartFraction 77 Over 85 EndFraction, cos

Likurg_2 [28]

Trigonometric functions are the ratio of the different sides of a right-angled triangle. We can say that the coordinates of the point are (-77, 36).

<h3>What are trigonometric functions?</h3>

Trigonometric functions are the ratio of the different sides of a right-angled triangle.

$\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Tan \theta=\dfrac{Perpendicular}{Base}$

where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite to the 90° angle.

Given to us

$Sin(\theta) = \dfrac{-77}{85}$

$Cos(\theta) = \dfrac{36}{85}$

$Tan(\theta) = \dfrac{-77}{36}$

As we know that the Tangent(Tan) is the ratio of perpendicular and base. therefore, we can write the function as,

$\rm Tan(\theta) = \dfrac{Perpendicular}{Base} = \dfrac{-77}{36}$

therefore, the length of the perpendicular is 77, while the length of the base is 36.

As given to us that the value of sin is negative, therefore, the perpendicular will be on the negative side of the y-axis. While the value of cos is positive, therefore, the base will be on the positive side of the x-axis.

Thus, we can say that the coordinates of the point are (-77, 36).

Learn more about Trigonometric functions:

brainly.com/question/6904750

8 0

2 years ago

Read 2 more answers