Mathematics, 20.12.2019 05:31 nique1024

Asample of eight workers in a clothing manufacturing company gave the following figures for the amount of time(in minutes) needed to join a collar to a shirt11 13 14 10 9 16 11 12construct a 95% confidence interval for the true mean amount of time needed to join a collar.

Answers: 3

Show answers

Answers

Answer from: viktoria1198zz

$10.108 < \mu < 13.892$

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".

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

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size

We have the following distribution for the random variable:

$X \sim N(\mu , \sigma=0.45)$

And by the central theorem we know that the distribution for the sample mean is given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

2) Confidence interval

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 mean and the sample deviation we can use the following formulas:

$\bar X= \sum_{i=1}^n \frac{x_i}{n}$ (2)

$s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}$ (3)

The mean calculated for this case is $\bar X=12$

The sample deviation calculated s=2.268

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

df=n-1=8-1=7

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 tabel to find the critical value. The excel command would be: "=-T.INV(0.025,7)".And we see that $t_{\alpha/2}=2.36$

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

$12-2.36\frac{2.268}{\sqrt{8}}=10.108$

$12+2.36\frac{2.268}{\sqrt{8}}=13.892$

So on this case the 95% confidence interval would be given by (10.108;13.892)

$10.108 < \mu < 13.892$

Answer from: Quest

took the test it's 94

Answer from: Quest

amount of oatypop that contains the prize = 40%

amount of oatypop which doesn't contain the prize = (100-40)=60%

probability that hannah will win a prize

= s +f s +f f s+ff f s+ff f f s+ infinity.where f= failure,s= success

= or 60%

probability that hannah only has to buy 3 or less boxes before getting a prize= (s) and ( f s) and (ff s) and (f f f s)

= = 87.04 %

step-by-step explanation:

Another question on Mathematics

Mathematics, 21.06.2019 15:00

Which sum or difference identity would you use to verify that cos (180° - ∅) = -cos ∅? a. sin (α -β) = sin α cos β – cos α sin β b. cos (α -β) = cos α cos β – sin α sin β c. cos (α -β) = cos α cos β + sin α sin β d. sin (α + β) = sin α cos β + cos α sin β

Answers: 2

Answer

Mathematics, 21.06.2019 17:00

Acar travels at an average speed of 56 miles per hour. how long does it take to travel 196 miles

Answers: 1

Answer

Mathematics, 21.06.2019 18:00

Agroup of students want to create a garden. they do not know the exact measurements but they propose using a variable to represent the length and width of the garden. the length of the garden is 10 feet longer than double the width. use a single variable to write algebraic expressions for both the length and width of the garden. write an algebraic expression for the area of the garden. use mathematical terms to describe this expression.

Answers: 3

Answer

Mathematics, 21.06.2019 21:50

What is the missing reason in the proof? segment addition congruent segments theorem transitive property of equality subtraction property of equality?

Answers: 3

Answer

You know the right answer?

Asample of eight workers in a clothing manufacturing company gave the following figures for the amou...

Questions

Mathematics, 30.12.2020 22:20

The equation y = 3x + 7 is written in slope-intercept form. O True False...

Mathematics, 30.12.2020 22:20

Zoey has 99 years .She plans to make 5 bangles .Each bangle is made using 30 beads how many more beads does zoey need?...