Show the work please

Mathematics

1 answer:

Neporo4naja [7]3 years ago

3 0

False, False, True
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The first is false since the square root of 19 is 4 and 4/7 is not a whole number

The second is false since the square root of 40 is 6.32 which is less than 7

The last is true because the square root of 30 is 5.48 and that makes the fraction equal 3.65 which again is a whole number while 2/3 is not

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Komok [63]

Answer: Correct critical value = 2.2622

Step-by-step explanation:

Confidence interval for population mean when population standard deviation is unknown:

$\overline{x}\pm t_{\alpha/2}\dfrac{s}{\sqrt{n}}$ , where $\overline{x}$ = sample mean, n= sample size, s= sample standard deviation, $t_{\alpha/2}$ = two-tailed t value.

As per given: n= 10

degree of freedom : df = n-1=9

$\overline{x}=242.6\\\\s=73.33\\\\\alpha=5\%=0.05$

Critical t-value : $t_{\alpha/2,df}=t_{0.05/2,9}=t_{0.025,9}=2.2622$

So, the 95 percent confidence interval estimate for the mean :

$242.6\pm (2.2622)\dfrac{73.33}{\sqrt{10}}\\\\=242.6\pm (2.2622)(23.19)\\\\\approx242.6\pm52.46\\\\=(242.6-52.46,\ 242.6+52.46)\\\\=(190.14,\ 295.06)$