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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

3 years ago

the angle of elevation of the top of a building from a point 80 ft away from the building on level ground is 70° determine the b

MA_775_DIABLO [31]

Draw a triangle with shortest side on the ground (horiz.). The length of this side is 80 feet. Two angles touch the ground: a right angle, and the 70 degree angle.

Then the height of the building is the 2nd shortest side.

The tangent function is the appropriate one to use here:
opp h
tan 70 deg = -------- = ----------
adj 80 ft
h
Since tan 70 deg = 2.75, 2.75 = -------
80 ft

so h = building height = (80 ft)(2.75) = 219.8 ft

6 0

3 years ago

Mario transferred a balance of $6050 to a new credit card at the beginning of

Kryger [21]

Answer:

the answer is (6050){1+0.031/12}^3{1+0.206/12}^9 for APEX

Step-by-step explanation:

7 0

2 years ago

Read 2 more answers

What is the fifth term of the geometric sequence? 5, 15 , 45, ...

Virty [35]

The geometry sequence has the equation $a(n)=5(3^{n-1})$ .

The 5 represents the first number of the sequence and the 3 represents the common ratio.

a(5) = $5(3^{5-1})=5(3^{4})=5(81)=405$

answer: 405

6 0

3 years ago

Use the equation y = 7x to complete the table. What are the missing values of

storchak [24]

Answer:

Option D

Step-by-step explanation:

In this table, the constant of proportionality, which is just the number that each x value is multiplied by to get the corresponding y value, is 7. This is because, as shown by the first row of the table, 1*7=7, and, as shown by the third row of the table, 3*7=21. Therefore, in the second row of the table, y should be 14, as 2*7=14, while in the fourth row of the table, y should be 28, as 4*7=28.

Hope this helps! Comment any questions.

8 0

2 years ago

Read 2 more answers