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

answer: the value of x is 7cm

step-by-step explanation:

The value of x is? hurry my test is gonna end in 5 min

Answer from: Quest

well what did you do it matters what you did : )

step-by-step explanation:

Another question on Mathematics

Mathematics, 21.06.2019 18:00

The given dot plot represents the average daily temperatures, in degrees fahrenheit, recorded in a town during the first 15 days of september. if the dot plot is converted to a box plot, the first quartile would be drawn at __ , and the third quartile would be drawn at link to the chart is here

Answers: 1

Answer

Mathematics, 21.06.2019 18:40

Acircle has a circumference of 28.36 units what is the diameter of the circle

Answers: 2

Answer

Mathematics, 21.06.2019 21:30

Handsome jack is buying a pony made of diamonds. the price of the pony is p dollars, and jack also has to pay a 25% diamond pony tax. which of the following expressions could represent how much jack pays in total for the pony?

Answers: 1

Answer

Mathematics, 22.06.2019 01:00

Acredit union pays 5% annual interest, compounded daily, on saving deposits. find the value after one year of $500 deposited in this account. a-$20.40 b-$25.64 c-$520.40 d-$525.64

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