Can someone help with 29, 30, 31, and 32 please!

A theory predicts that the mean age of stars within a particular type of star cluster is 3.3 billion years, with a standard devi

Luden [163]

Answer:

Null hypothesis: $\mu \leq 3.3$

Alternative hypothesis: $\mu > 3.3$

$z=\frac{3.4-3.3}{\frac{0.4}{\sqrt{50}}}=1.768$

Since is a one right tailed test the p value would be:

$p_v =P(z>1.768)=0.039$

Step-by-step explanation:

Data given and notation

$\bar X=3.4$ represent the sample mean

$\sigma=0.4$ represent the population deviation for the sample

$n=50$ sample size

$\mu_o =3.3$ represent the value that we want to test

$\alpha$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

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

State the null and alternative hypotheses to be tested

We need to conduct a hypothesis in order to determine if the mean is higher than 3.3, the system of hypothesis would be:

Null hypothesis: $\mu \leq 3.3$

Alternative hypothesis: $\mu > 3.3$

Compute the test statistic

We know the population deviation, so for this case is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

We can replace in formula (1) the info given like this:

$z=\frac{3.4-3.3}{\frac{0.4}{\sqrt{50}}}=1.768$

P value

Since is a one right tailed test the p value would be:

$p_v =P(z>1.768)=0.039$

6 0

2 years ago

Kyle and Taylor ran laps after school to train for the baseball team. The ratio of the number of laps Kyle ran to the number of

Zinaida [17]

Answer:

9 laps.

Step-by-step explanation:

-Let x be the number of laps Taylor runs.

-Given that the ratio of Kyle to Taylor laps is 2:3, we express the actual laps in meters to solve for x as follows:

$\frac{Kyle}{Taylor}=\frac{2}{3}\\\\\therefore \frac{2}{3}=\frac{6}{x}\\\\2x=18\\\\x=9$

Hence, Taylor runs 9 laps.

4 0

3 years ago

1, 3,4,5,11, answer is 65 _ + (_-_)^2 +_x_

Y_Kistochka [10]

Answer:

1 + (11-4)^2 +3x5

Step-by-step explanation:

1 + (11-4)^2 +3x5

1 + (7)^2 + 3 x 5

1 + 49 + 15

50 + 15 = 65

5 0

2 years ago

The magnitude and direction of two vectors are shown in the diagram. What is the magnitude of their sum?

VLD [36.1K]

Separate the vectors into their x- and y-components. Let u be the vector on the right and v the vector on the left, so that

u = 4 cos(45°) x + 4 sin(45°) y

v = 2 cos(135°) x + 2 sin(135°) y

where x and y denote the unit vectors in the x and y directions.

Then the sum is

u + v = (4 cos(45°) + 2 cos(135°)) x + (4 sin(45°) + 2 sin(135°)) y

and its magnitude is

||u + v|| = √((4 cos(45°) + 2 cos(135°))² + (4 sin(45°) + 2 sin(135°))²)

… = √(16 cos²(45°) + 16 cos(45°) cos(135°) + 4 cos²(135°) + 16 sin²(45°) + 16 sin(45°) sin(135°) + 4 sin²(135°))

… = √(16 (cos²(45°) + sin²(45°)) + 16 (cos(45°) cos(135°) + sin(45°) sin(135°)) + 4 (cos²(135°) + sin²(135°)))

… = √(16 + 16 cos(135° - 45°) + 4)

… = √(20 + 16 cos(90°))

… = √20 = 2√5

5 0

2 years ago

Read 2 more answers

What does n^9/n^5 equal

vovangra [49]

Answer:

$n^4$

Step-by-step explanation:

Rule:

$\dfrac{a^m}{a^n} = a^{m - n}$

Your problem:

$\dfrac{n^9}{n^5} = n^{9 - 5} = n^4$

4 0

3 years ago