Mathematics, 07.04.2020 19:35 Suzispangler2264

The output voltage for an electric circuit is specified to be 127 volts. A sample of 40 independent readings on the voltage for this circuit gave a sample mean 125.8 volts and standard deviation 2 volts. Test the hypothesis that the average output voltage is 127 volts against the alternative that it is less than 127 volts. Use a test with level 0.05. State the null and alternative hypotheses.

Answers: 3

Show answers

Answers

Answer from: cailynrachael

$t=\frac{125.8-127}{\frac{2}{\sqrt{40}}}=-3.795$

$p_v =P(t_{(39)}$

If we compare the p value and the significance level given $\alpha=0.05$ we see that p_v so we can conclude that we have enough evidence to reject the null hypothesis, we can conclude that the true mean is significantly les than 127 at 5% of signficance.

Step-by-step explanation:

Data given and notation

$\bar X=125.8$ represent the sample mean

s=2 represent the sample standard deviation

n=40 sample size

$\mu_o =127$ 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 ture mean is less than 127 or no, the system of hypothesis would be:

Null hypothesis: $\mu = 127$

Alternative hypothesis: $\mu < 127$

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:

$t=\frac{125.8-127}{\frac{2}{\sqrt{40}}}=-3.795$

P-value

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

df=n-1=40-1=39

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

$p_v =P(t_{(39)}$

Conclusion

Answer from: Quest

logv3(x+2)=1

rewrite in exponential form:

logb(x) = y is equal to b^y =x

b = 3, y = 1

now solve for x:

3^1 = x+2)

x = 3-2

x = 1

see the picture for the graph.

Answer from: Quest

B-simple yes/no questions

Another question on Mathematics

Mathematics, 21.06.2019 20:30

What is always true about a positive integer raised to a negative odd power?

Answers: 1

Answer

Mathematics, 21.06.2019 23:00

Solve the system of equations using the substitution method. {y=−3x+7x=−2y−16 enter your answers in the boxes.

Answers: 1

Answer

Mathematics, 22.06.2019 01:30

Sandy is upgrading her internet service. fast internet charges $20 for installation and $52.45 per month. quick internet has free installation but charges $57.45 per month. part 1 out of 2 complete the equation that can be used to find the number of months after which the internet service would cost the same. use the variable x to represent the number of months of internet service purchased.

Answers: 1

Answer

Mathematics, 22.06.2019 06:50

Convert the polar representation of this complex number into its rectangular form: z=5(cos pi+i sin pi)

Answers: 2

Answer

You know the right answer?

The output voltage for an electric circuit is specified to be 127 volts. A sample of 40 independent...

Questions