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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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The diameter of a circle is 10 cm what is the angle measure of an arc Pi centimeters long
vredina [299]
We know that

[length of a circumference]=2*pi*r
diameter=10 cm
r=10/2-----> 5 cm
[length of a circumference]=2*pi*5-----> 10*pi cm

if 360° (full circle) has a length of -----------> 10*pi cm
 X°---------------------------> pi cm
X=pi*360/10*pi------> 36°

the answer is 36°
8 0
3 years ago
Mrs. Reed collects shells. Each shell in her collection weighs about 4 ounces. Her collection weighs about 12 pounds in all. Abo
Mariana [72]

Answer:

There are about 48 shells in Mrs. Reeds collection.

Step-by-step explanation:

There are 16 ounces per 1 pound.

4 ounces per shell.

16 x 12 = 192 ounces

192 ounces divided by 4 = 48

8 0
2 years ago
$300 at 6% for 3 years
Charra [1.4K]
Its I=prt 
so plug it in
I=300(.06)3 i got .06 because you have 6% you have to move the decimal  the left twice 0.06 is what you get
now its basic multiplying
300 times .06 times 3
so it would be 54
I=$54
the balence you get from adding the P to the I so the balence would be 356
Bal=$356
7 0
3 years ago
Consider the following statement: The square of a prime number is not prime. (a) Write this as an if-then statement, using caref
Hitman42 [59]

The square of a prime number is not prime.

a) let x ∈ R, If x  ∈ {prime numbers}, then x^{2}∉{prime numbers}

there says that if x is a real and x is in the set of the prime numbers, then the square of x isn't in the set of prime numbers.

b) Prove or disprove the statement.

ok, if x is a prime number, then x only can be divided by himself. Now is easy to see that x^{2} = x*x can be divided by himself and x, then x*x is not a prime number, because can be divided by another number different than himself

7 0
3 years ago
A math class is having a discussion on how to determine if the expressions 4 x minus x + 5 and 8 minus 3 x minus 3 are equivalen
Brut [27]

Answer:

  • Both expressions should be evaluated with two different values. If for each substituted value, the final values of the expressions are the same, then the two expressions must be equivalent.

Step-by-step explanation:

<u>Given expressions</u>

  • 4x - x + 5 = 3x + 5
  • 8 - 3x - 3 = -3x + 5

Compared, we see the expressions are different as 3x and -3x have different coefficient

<u>Answer options</u>

Both expressions should be evaluated with one value. If the final values of the expressions are both positive, then the two expressions must be equivalent.

  • Incorrect. Positive outcome doesn't mean equivalent

----------------------------------------

Both expressions should be evaluated with one value. If the final values of the expressions are the same, then the two expressions must be equivalent.

  • Incorrect. There are 2 values- variable and constant

----------------------------------------

Both expressions should be evaluated with two different values. If for each substituted value, the final values of the expressions are positive, then the two expressions must be equivalent.

  • Incorrect. Positive outcome doesn't mean equivalent.

----------------------------------------

Both expressions should be evaluated with two different values. If for each substituted value, the final values of the expressions are the same, then the two expressions must be equivalent.

  • Correct.  
3 0
3 years ago
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