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.

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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

answer: all of the odd numbers were opened

the first person was the one that was opening all of the lockers. since one is odd, this causes all of the odd number lockers to be opened in the end.

Answer from: Quest

the data of the detroit pistons in numerical order from least to greatest is 0.30, 0.37, 0.55, 0.62, 0.69, 0.72, 0.73, 0.75, 0.77, 0.78, 0.80, 0.81, 0.81, 0.83, 0.84, 0.89

the data of the miami heat in numerical order from least to greatest is 0.50, 0.50, 0.56, 0.57, 0.67, 0.72, 0.72, 0.72, 0.75, 0.75, 0.76, 0.81, 0.82, 0.90, 1.00, 1.00

the detroit pistons median : 1.52

the miami heat median: 1.47

the iqr of this data is 0.05

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