Mathematics: In a random sample of 7 residents of the state of Maine, the mean waste recycled per person per day was 1.4 pounds with a standard deviation of 0.23 pounds. Determine the 95% confidence interval for the mean waste recycled per person per day for the population of Maine. Assume the population is approximately normal. Step 1 of 2 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.

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In a random sample of 7 residents of the state of

Ответ:

mfin11

29.01.2022

df=n-1=7-1=6

The Confidence desired is 0.95 or 95%, then the significance is $\alpha=0.05$ and $\alpha/2 =0.025$ , and the critical value in the t distribution with 6 degrees of freedom would be $t_{\alpha/2}=2.447$

$1.4-2.447\frac{0.23}{\sqrt{7}}=1.187$

$1.4+2.447\frac{0.23}{\sqrt{7}}=1.613$

The 95% confidence interval for the true mean would be between (1.187;1.613)

Step-by-step explanation:

Information given

$\bar X =1.4$ represent the sample mean

$\mu$ population mean (variable of interest)

s=0.23 represent the sample standard deviation

n=7 represent the sample size

Confidence interval

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

The degrees of freedom are given by

df=n-1=7-1=6

Now replacing we got:

$1.4-2.447\frac{0.23}{\sqrt{7}}=1.187$

$1.4+2.447\frac{0.23}{\sqrt{7}}=1.613$

The 95% confidence interval for the true mean would be between (1.187;1.613)

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