Find the value of x please

Mathematics

2 answers:

snow_tiger [21]3 years ago

8 0

<span>x=11.47153 is the correct answer.
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Elena L [17]3 years ago

6 0

X=11.47153 is the answer.

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A random sample of 42 college graduates who worked during their program revealed that a student spent an average 5.5 years on th

Neko [114]

Answer:

$5.5-2.701\frac{1.1}{\sqrt{42}}=5.04$

$5.5+2.701\frac{1.1}{\sqrt{42}}=5.96$

So on this case the 99% confidence interval would be given by (5.04;5.96)

And the best option would be:

a. 5.04 and 5.96

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".

$\bar X=5.5$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s=1.1 represent the sample standard deviation

n=42 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:

$df=n-1=42-1=41$

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(0.005,41)".And we see that $t_{\alpha/2}=2.701$