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alexdok [17]
3 years ago
10

A study was recently conducted to estimate the mean cholesterol for adult males over the age of 55 years. From a random sample o

f n10 ​men, the sample mean was found to be 242.6 and the sample standard deviation was 73.33. To find the 95 percent confidence interval estimate for the​ mean, what is the correct critical value to​ use?
Mathematics
1 answer:
Komok [63]3 years ago
8 0

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)

The 95 percent confidence interval estimate for the​ mean:(190.14, 295.06)

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Answer:

Volume, V = 3367.6 cm³

Step-by-step explanation:

Given the following data;

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To find the volume of the sphere;

Mathematically, the volume of a sphere is given by the formula;

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Where;

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Substituting into the formula, we have;

V = \frac {4}{3} * 3.14 * 9.3^{3}

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Volume, V = 3367.6 cm³

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2 years ago
In the triangle below, angle B measures 60° and BC is 18. What is the length of AC?
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6 0
3 years ago
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An isosceles triangle has an angle that measures 38degrees. What measures are possible for the other two angles? Choose all that
Sphinxa [80]

Answer:

  • 71° and 71°.

⠀

Step-by-step explanation:

The triangle having two sides equal along with one different side is called an isosceles triangle.

⠀

  • So, Let us assume the other sides (two equal sides) of the isosceles triangle as x. As the different side is already given in the question.

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We know that,

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So, According to the question :

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{\longrightarrow \it\qquad { \ { {  38 \: }^{ \circ}   + x + x  =  180{}^{ \circ} }}}

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{\longrightarrow \it\qquad { \ { {  38 \: }^{ \circ}   + 2x   =  180{}^{ \circ} }}}

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{\longrightarrow \it\qquad { \ {   2x   =  180{}^{ \circ} - {  38 \: }^{ \circ}}}}

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{\longrightarrow \it\qquad { \ {   2x   =  142{}^{ \circ}  }}}

⠀

{\longrightarrow \it\qquad { \ {   x   =    \dfrac{142{}^{ \circ}}{2}   }}}

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{\longrightarrow \it\qquad { \pmb {   x   =  71^{ \circ}  }}}

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Therefore,

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2 years ago
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Ahat [919]

Answer:

E) 6

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a/b = 6

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2 years ago
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