Mathematics, 23.01.2020 22:31 shongmadi77

You research commute times to work and find that the population standard deviation is 9.3 minutes. repeat exercise, using the standard normal distribution with the appropriate calculations for a standard deviation that is known. compare the results. in a random sample of eight people, the mean commute time to work was 35.5 minutes and the standard deviation was 7.2 minutes.

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Answer from: xxmattieboo7xx

Case s =7.2

$35.5-2.36\frac{7.2}{\sqrt{8}}=29.49$

$35.5+2.36\frac{7.2}{\sqrt{8}}=41.51$

So on this case the 95% confidence interval would be given by (29.49;41.51)

Case $\sigma =9.3$

$35.5-1.96\frac{9.3}{\sqrt{8}}=29.06$

$35.5+1.96\frac{9.3}{\sqrt{8}}=41.94$

So on this case the 95% confidence interval would be given by (29.06;41.94)

And we conclude that the intervals are very similar.

Step-by-step explanation:

If we assume that for this question we need to find a confidence interval for the population mean. We have the following procedure:

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".

$\bar X= 35.5$ represent the sample mean

$\mu$ population mean (variable of interest)

s=7.2 represent the sample standard deviation

n=8 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=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 table 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):

$35.5-2.36\frac{7.2}{\sqrt{8}}=29.49$

$35.5+2.36\frac{7.2}{\sqrt{8}}=41.51$

So on this case the 95% confidence interval would be given by (29.49;41.51)

If we assume that the real population standard deviation is $\sigma =9.3$ the confidence interval is given by:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$

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: "=-NORM.INV(0.025,0,1)".And we see that $z_{\alpha/2}=1.96$

$35.5-1.96\frac{9.3}{\sqrt{8}}=29.06$

$35.5+1.96\frac{9.3}{\sqrt{8}}=41.94$

So on this case the 95% confidence interval would be given by (29.06;41.94)

And we conclude that the intervals are very similar.

Answer from: Quest

the equation cos(35) =a/25 can be used to find the length of bc what is the length of bc? round to the nearest tenth

step-by-step explanation:

Answer from: Quest

think about the doctor who treated the major and the speaker in the short story "in another country." put yourself in the shoes of the doctor, and based on what you read in the story, write what you think his thoughts about the major and the speaker would be. use the following vocabulary in your response and change the form of these words as needed: detached resign withered