Mathematics, 27.02.2020 18:00 Hehdjdvgs8464

The viscosity of a liquid detergent is supposed to average 800 centistokes at 25° C. A random sample of 16 batches of detergent is collected, and the average viscosity is 812. Suppose we know that the standard deviation of viscosity is o = 25 centistokes: (a) State the hypotheses that should be tested, (b) Test these hypotheses using a = 0.05. What are your conclusions?, (c) What is the P-value for the test?,(d) Find a 95 percent confidence interval on the mean.

Answers: 2

Show answers

Answers

Answer from: Mordred4987

a) Null hypothesis: $\mu = 800$

Alternative hypothesis: $\mu \neq 800$

b) $z=\frac{812-800}{\frac{25}{\sqrt{16}}}=1.92$

c) p_v =2*P(z1.92)=0.0548

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 FAIL to reject the null hypothesis, and the the actual mean is not different from the value of 800.

d) $812- 1.96 \frac{25}{\sqrt{16}}=799.75$

$812+ 1.96 \frac{25}{\sqrt{16}}=824.25$

Since the confidence interval contains the value 800 this result agrees with the result obtained in the hypothesis test we fail to reject the null hypothesis that the true mean is 800

Step-by-step explanation:

Data given and notation

$\bar X=812$ represent the mean for the sample

$\sigma=25$ represent the standard deviation for the population

n=16 sample size

$\mu_o =800$ represent the value that we want to test

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

z would represent the statistic (variable of interest)

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

a) State the null and alternative hypotheses.

We need to conduct a hypothesis in order to determine if the true mean is different from 800 centistokes:

Null hypothesis: $\mu = 800$

Alternative hypothesis: $\mu \neq 800$

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".

b) Calculate the statistic

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

$z=\frac{812-800}{\frac{25}{\sqrt{16}}}=1.92$

c) Calculate the P-value

Since is a two tailed test the p value would be:

p_v =2*P(z1.92)=0.0548

Conclusion

d) Confidence interval

The confidence interval for the mean is given by the following formula:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

For the 95% confidence interval the value of $\alpha=1-0.95=0.05$ and $\alpha/2=0.025$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=1.96$

And replacing we got:

$812- 1.96 \frac{25}{\sqrt{16}}=799.75$

$812+ 1.96 \frac{25}{\sqrt{16}}=824.25$

Since the confidence interval contains the value 800 this result agrees with the result obtained in the hypothesis test we fail to reject the null hypothesis that the true mean is 800

Answer from: Quest

1. 8 or -82. 14 or -143. -11, -3, 0, 7, 10

Answer from: Quest

he sells x mount because thats eqivilqant to the maz and then divided into quarters

step-by-step explanation:

Another question on Mathematics

Mathematics, 21.06.2019 19:00

The lengths of all sides of a triangle are integers when measured in decimeters. one of the sides has length of 1 dm and another of 3 dm. find the perimeter of the triangle.'

Answers: 1

Answer

Mathematics, 21.06.2019 21:10

If f(x) and g(x) are inverse functions of each other, which of the following shows the graph of f(g(x)

Answers: 1

Answer

Mathematics, 21.06.2019 22:00

Match the scale and the actual area to the area of the corresponding scale drawing. scale: 1 inch to 4 feet actual area: 128 square feet scale: 1 inch to 7 feet actual area: 147 square feet scale: 1 inch to 8 feet actual area: 256 square feet scale: 1 inch to 5 feet actual area: 225 square feet area of scale drawing scale and actual area scale drawing area: 3 square inches arrowright scale drawing area: 8 square inches arrowright scale drawing area: 4 square inches arrowright scale drawing area: 9 square inches arrowright

Answers: 2

Answer

Mathematics, 21.06.2019 23:00

Mr. rose asked his students to draw a quadrilateral with 4 unequal sides. draw an example of this kind of quadrilateral.

Answers: 2

Answer

You know the right answer?

The viscosity of a liquid detergent is supposed to average 800 centistokes at 25° C. A random sample...

Questions