Mathematics, 23.01.2020 19:31 sbanoali2896

Arandom sample of 225 measurements is selected from a population, and the sample mean and standard deviation are x =32.5 and s = 30.0, respectively. it is claimed that the population mean exceeds 30. state the null and an appropriate alternative hypothesis, and perform a test at 5% significance level.

Answers: 3

Show answers

Answers

Answer from: ComicSans10

$t=\frac{32.5-30}{\frac{30}{\sqrt{225}}}=1.25$

$p_v =P(t_{(224)}1.25)=0.106$

If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, so we can't conclude that the true mean is actually its significantly higher than 30.

Step-by-step explanation:

Data given and notation

$\bar X=32.5$ represent the sample mean

s=30 represent the sample standard deviation

n=225 sample size

$\mu_o =30$ represent the value that we want to test

$\alpha=0.05$ 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.

We need to conduct a hypothesis in order to check if the mean exceeds 30, the system of hypothesis would be:

Null hypothesis: $\mu \leq 30$

Alternative hypothesis: $\mu 30$

If we analyze the size for the sample is > 30 but we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-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".

Calculate the statistic

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

$t=\frac{32.5-30}{\frac{30}{\sqrt{225}}}=1.25$

P-value

The first step is calculate the degrees of freedom, on this case:

df=n-1=225-1=224

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

$p_v =P(t_{(224)}1.25)=0.106$

Conclusion

Answer from: Quest

we need more info to solve this

Answer from: Quest

you might have to contact customer support. if you have it on your iphone you just got into your settings> subscriptions> cancel

step-by-step explanation:

Another question on Mathematics

Mathematics, 22.06.2019 02:30

Atriangle has side lengths of x, x+11, and 3x+5. what is the perimeter? a. 3x^2 + 38x + 55 b. 4x + 16 c. 5x + 16 d. 3x^3 + 38x^2 + 55x

Answers: 1

Answer

Mathematics, 22.06.2019 03:00

Which is the graph of the following inequality?

Answers: 3

Answer

Mathematics, 22.06.2019 03:40

Vikram is studying the square pyramid below. on st to find the surface area of the pyramid, in square inches, vikram wrote (33.2) (34 ikram wrote (33.2)(34.2)+43(34.2)(284) what error did vikram make? o he used the same expression for the area of all four lateral faces. he used the wrong expression to represent the area of the base of the pyramid. o he used the wrong value as the height when he found the area of the lateral faces. he used an expression for surface area that only finds the total area of three faces.

Answers: 3

Answer

Mathematics, 22.06.2019 04:00

Radials are weird[tex](14 \sqrt{6}) ^{2} [/tex]whats the answer and how do i solve pls

Answers: 1

Answer

You know the right answer?

Arandom sample of 225 measurements is selected from a population, and the sample mean and standard d...

Questions