Mathematics, 12.02.2020 02:57 help1219

A random sample of 110 lightning flashes in a certain region resulted in a sample average radar echo duration of .81 seconds and a sample standard deviation of .34 seconds. Calculate a 99% (two-sided) confidence interval for the true average echo duration μ, and interpret the resulting interval.

Answers: 1

Show answers

Answers

Answer from: ahrozycki

$0.81-2.62\frac{0.34}{\sqrt{110}}=0.725$

$0.81+2.62\frac{0.34}{\sqrt{110}}=0.895$

So on this case the 99% confidence interval would be given by (0.725;0.895)

We are confident 99% that the true mean for the echo duration is between 0.725 and 0.895 seconds

Step-by-step explanation:

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".

$\bar X= 0.81$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s=0.34 represent the sample standard deviation

n =110 represent the sample size

Solution to the problem

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=110-1=109

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(0.005,109)".And we see that $t_{\alpha/2}=2.62$

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

$0.81-2.62\frac{0.34}{\sqrt{110}}=0.725$

$0.81+2.62\frac{0.34}{\sqrt{110}}=0.895$

So on this case the 99% confidence interval would be given by (0.725;0.895)

We are confident 99% that the true mean for the echo duration is between 0.725 and 0.895 seconds

Answer from: Quest

The answer that i got was 8/3

Answer from: Quest

rick has $1400 and sally has $1500

step-by-step explanation:

to find amount of money rick has after 10 years :

principal = $1000 , time = 10 years , rate = 4% annually

$\text{simple interest} = \frac{principal\times rate\times time}{100} \\\\\text{simple interest} = \frac{1000\times 4\times 10}{100}=\$400\\\\amount = principal + interest\\amount = 1000 + 400 = \$1400$

to find amount of money sally has after 10 years :

her friend gives to pay her $50 per year, therefore money she has after 10 years = 50 × 10 = $500

also, sally gets $1000 after 10 years,

therefore, total amount of money sally has after 10 years = 500 + 1000 = $1500

so, after 10 years : rick has $1400 and sally has $1500

Another question on Mathematics

Mathematics, 21.06.2019 16:00

The scatter plot graph shows the average annual income for a certain profession based on the number of years of experience which of the following is most likely to be the equation of the trend line for this set of data? a. i=5350e +37100 b. i=5350e-37100 c. i=5350e d. e=5350e+37100

Answers: 1

Answer

Mathematics, 21.06.2019 21:00

Can someone answer this question for me

Answers: 1

Answer

Mathematics, 21.06.2019 23:00

Analyze the diagram below and complete the instructions that follow. how to find tan

Answers: 2

Answer

Mathematics, 22.06.2019 00:30

What is the solution for 6 - 7/8? explain the steps.