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

Cbottom left is the correct one.
Question 4) which table does not represent a linear function?

Answer from: Quest

anser is a

step-by-step explanation:

negitive slope

Fast! plz will list ! 1. what set of points on the given graph

Another question on Mathematics

Mathematics, 21.06.2019 13:00

Renita analyzed two dot plots showing the snowfall during the winter months for city a and for city b. she found that the median snowfall is 5 inches less in city a than in city b. the mean snowfall is about 2 inches less in city a than in city b. which explains why there is a difference in the measures of center for the sets of data?

Answers: 3

Answer

Mathematics, 21.06.2019 15:00

What is the multiplicative rate of change of the exponential function shown on the graph?

Answers: 2

Answer

Mathematics, 21.06.2019 15:30

Find the gradient of f(x,y,z)equals=left parenthesis x squared plus y squared plus z squared right parenthesis superscript negative 1 divided by 2 baseline plus ln left parenthesis x right parenthesis x2+y2+z2−1/2+ln(xyz) at the point left parenthesis negative 2 comma 1 comma negative 2 right parenthesis(−2,1,−2).

Answers: 1

Answer

Mathematics, 21.06.2019 18:30

Need an artist designed a badge for a school club. figure abcd on the coordinate grid below shows the shape of the badge: the badge is enlarged and plotted on the coordinate grid as figure jklm with point j located at (2, -2) and point m is located at (5, 4). which of these could be the coordinates for point l? a. (2, 4) b. (8, 4) c. (5, 1) d. (5, 7)

Answers: 2

Answer

You know the right answer?

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

Questions

Mathematics, 23.10.2020 01:01

Can Someone Help Me. ? ...

Mathematics, 23.10.2020 01:01

Help me please please ...