Mathematics, 12.12.2019 23:31 nerissa5

Each of 20 science students independently measured the melting point of lead. the sample mean and sample standard deviation of these measurements were (in degrees centigrade) 330.2 and 15.4, respectively. construct

(a) a 95 percent confidence interval estimate of the true weight.

(b) a 99 percent confidence interval estimate of the true melting point of lead.

Answers: 3

Show answers

Answers

Answer from: TookMurr

a) The 95% confidence interval would be given by (323.003;337.397)

b) The 99% confidence interval would be given by (320.351;340.049)

Step-by-step explanation:

1) Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X=330.2$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s=15.4 represent the sample standard deviation

n=20 represent the sample size

2) Part a

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

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

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

df=n-1=20-1=19

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,19)".And we see that $t_{\alpha/2}=2.09$

Now we have everything in order to replace into formula (1):

$330.2-2.09\frac{15.4}{\sqrt{20}}=323.003$

$330.2+2.09\frac{15.4}{\sqrt{20}}=337.397$

So on this case the 95% confidence interval would be given by (323.003;337.397)

3) Part b

Since the Confidence is 0.99 or 99%, the value of $\alpha=0.01$ and $\alpha/2 =0.005$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,19)".And we see that $t_{\alpha/2}=2.86$

Now we have everything in order to replace into formula (1):

$330.2-2.86\frac{15.4}{\sqrt{20}}=320.351$

$330.2+2.86\frac{15.4}{\sqrt{20}}=340.049$

So on this case the 99% confidence interval would be given by (320.351;340.049)

Answer from: Quest

7! = 7×6×5×4×3×2

3! = 3× 2

as 7! is multiple of 3! because 7! contains 3! that is 3× 2 as factor

so 7! /(3! ) = 7× 6× 5× 4

= 42 × 20

= 840

its b) 840✌✌✌

dhruv⭐

Answer from: Quest

ed sheeran was one of the winners?

step-by-step explanation:

google xd

Another question on Mathematics

Mathematics, 20.06.2019 18:02

Ared balloon starts at 7.3 meters off the ground and rises at 2.6 meters per second. a blue balloon starts at 12.4 meters off the ground and rises at 1.5 meters per second. when will the balloons be at the same height?

Answers: 1

Answer

Mathematics, 20.06.2019 18:04

Dr.cooper just started an experiment. he will collect data for 8 days. how many hours is this

Answers: 2

Answer

Mathematics, 21.06.2019 17:00

Asays "we are both knaves" and b says nothing. exercises 24–31 relate to inhabitants of an island on which there are three kinds of people: knights who always tell the truth, knaves who always lie, and spies (called normals by smullyan [sm78]) who can either lie or tell the truth. you encounter three people, a, b, and c. you know one of these people is a knight, one is a knave, and one is a spy. each of the three people knows the type of person each of other two is. for each of these situations, if possible, determine whether there is a unique solution and determine who the knave, knight, and spy are. when there is no unique solution, list all possible solutions or state that there are no solutions. 24. a says "c is the knave," b says, "a is the knight," and c says "i am the spy."

Answers: 2

Answer

Mathematics, 21.06.2019 18:00

Negative 5 1/12 + negative 4 1/4 + 6 3/4

Answers: 1

Answer

You know the right answer?

Each of 20 science students independently measured the melting point of lead. the sample mean and sa...

Questions