C = z-q/a for ‎z‎ (Integrated Math 8)

Mathematics

1 answer:

Trava [24]3 years ago

7 0

Answer:z=c+q/a

Step-by-step explanation:

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$\frac{(17)(0.038)^2}{32.64} \leq \sigma^2 \leq \frac{(17)(0.038)^2}{6.66}$

$0.0008 \leq \sigma^2 \leq 0.0037$

Step-by-step explanation:

Data given and notation

s=0.038 represent the sample standard deviation

$\bar x$ represent the sample mean

n=18 the sample size

Confidence=97.5% or 0.975

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 mean or variance 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.

The Chi Square distribution is the distribution of the sum of squared standard normal deviates .

Calculating the confidence interval

The confidence interval for the population variance is given by the following formula:

$\frac{(n-1)s^2}{\chi^2_{\alpha/2}} \leq \sigma^2 \leq \frac{(n-1)s^2}{\chi^2_{1-\alpha/2}}$

The next step would be calculate the critical values. First we need to calculate the degrees of freedom given by:

$df=n-1=18-1=17$

Since the Confidence is 0.975 or 97.5%, the value of $\alpha=0.025$ and $\alpha/2 =0.0125$ , and we can use excel, a calculator or a table to find the critical values.