Mathematics, 24.06.2020 17:01 Jinesha

The percent, X, of shrinkage on drying for a certain type of plastic clay has an average shrinkage percentage :, where parameter : is unknown. A random sample of 45 specimens from this clay showed an average shrinking percentage of 18.4 and a standard deviation of 2.2. est at 5% level of significance whether the true average shrinkage percentage : is greater than 17.5 and write your conclusion. Report the p-value.

Answers: 3

Show answers

Answers

Answer from: sw2098

$t=\frac{18.4-17.5}{\frac{2.2}{\sqrt{45}}}=2.744$

The degrees of freedom are given by:

df=n-1=45-1=44

The critical value for this case is $t_{\alpha}=1.68$ since the calculated value is higher than the critical we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly higher than 18.4

$p_v =P(t_{(44)}2.744)=0.0044$

We see that the p value is lower than the significance level so then we can reject the null hypothesis in favor of the alternative.

Step-by-step explanation:

Information given

$\bar X=18.4$ represent the sample mean

s=2.2 represent the sample standard deviation

n=45 sample size

$\mu_o =17.5$ represent the value to verify

$\alpha=0.05$ represent the significance level

t would represent the statistic

p_v represent the p value

We want to test if the true mean is higher than 17.5, the system of hypothesis would be:

Null hypothesis: $\mu \leq 17.5$

Alternative hypothesis: $\mu 17.5$

The statistic is given by:

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

And replacing we got:

$t=\frac{18.4-17.5}{\frac{2.2}{\sqrt{45}}}=2.744$

The degrees of freedom are given by:

df=n-1=45-1=44

The p value would be given by:

$p_v =P(t_{(44)}2.744)=0.0044$

We see that the p value is lower than the significance level so then we can reject the null hypothesis in favor of the alternative.

Answer from: Quest

answer: the answer is (b) amie should have multiplied

$54~\textup{m}^3~\textup{by}~\dfrac{4}{3}\pi.$

step-by-step explanation: given a sphere and a cylinder with same radius and height.

let, 'r' be the radius of the cylinder and sphere and 'h' be the height of the cylinder. according to the question,

r = h.

now, the volume of the sphere will be

$v_s=\pi r^2h=\pi r^3,$

and the volume of the cylinder will be

$v_c=\dfrac{4}{3}\pi r^3=54~\textup{m}^3.$

therefore, we have

$v_c=\dfrac{4}{3}v_s=\dfrac{4}{3}\times 54=72~\textup{m}^3.$

thus, ammie should have multiplied the volume of the sphere $54~\textup{m}^3~\textup{by}~\dfrac{4}{3}\pi.$

Answer from: Quest

so far i think you have the right thing going for you just remember soh cah toh

step-by-step explanation:

sine over hypotenuse

cosine equals adjacent

tangent over hypotenuse

Special right triangles trig ratios and circles need i am studying for my test

Another question on Mathematics

Mathematics, 21.06.2019 20:00

A50% increase followed by 33 1/2% decrease

Answers: 3

Answer

Mathematics, 21.06.2019 22:00

Rewrite 9 log, x2 in a form that does not use exponents. 9log, x = log, x

Answers: 3

Answer

Mathematics, 22.06.2019 00:40

Point b lies between points a and c on . let x represent the length of segment ab in inches. use the segment to complete the statements. the value of x is . the length of in inches is . the length of in inches is .

Answers: 3

Answer

Mathematics, 22.06.2019 02:30

Harry owes the bank money. to repay his debt, he paid $150 back to the bank each month. after 10 months, his remaining debt was $6900. what was the original amount of harry's debt? how long did it take harry to pay back his entire debt?

Answers: 2

Answer

You know the right answer?

The percent, X, of shrinkage on drying for a certain type of plastic clay has an average shrinkage p...

Questions