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ollegr [7]
3 years ago
7

A professor would like to test the hypothesis that the average number of minutes that a student needs to complete a statistics e

xam has a standard deviation that is less than 5.0 minutes. A random sample of 15 students was selected and the sample standard deviation for the time needed to complete the exam was found to be 4.0 minutes. Using α = 0.05, the conclusion for this hypothesis test would be that because the test statistic is
Mathematics
1 answer:
professor190 [17]3 years ago
6 0

Answer:

\chi^2 =\frac{15-1}{25} 16 =8.96

The degrees of freedom are given by:

df = n-1 = 15-1=14

The p value for this case would be given by:

p_v =P(\chi^2

Since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true deviation is not ignificantly lower than 5 minutes

Step-by-step explanation:

Information given

n=15 represent the sample size

\alpha=0.05 represent the confidence level  

s^2 =16 represent the sample variance

\sigma^2_0 =25 represent the value that we want to  verify

System of hypothesis

We want to test if the true deviation for this case is lesss than 5minutes, so the system of hypothesis would be:

Null Hypothesis: \sigma^2 \geq 25

Alternative hypothesis: \sigma^2

The statistic is given by:

\chi^2 =\frac{n-1}{\sigma^2_0} s^2

And replacing we got:

\chi^2 =\frac{15-1}{25} 16 =8.96

The degrees of freedom are given by:

df = n-1 = 15-1=14

The p value for this case would be given by:

p_v =P(\chi^2

Since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true deviation is not ignificantly lower than 5 minutes

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Suppose you are given a cube made of magnesium (mg) metal of edge length 2.15 cm. (a) calculate the number of mg atoms in the cu
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solution:

a) To calculate the volume of cube of edge 1.0cm

Volume= (edge)³

=(100cm) ³

= 1cm³

To find the mass of MG atoms  

Density = mass/volume

Mass of mg = 1.74g/cm³ x 1cm³

       = 1.74g

To find the number of mg atoms,

Molar mass of mg = 24.31g

24.31g mg contain 6.022 x 10²³ atoms of mg  

1.74g mg contain = 6.022 x 10²³mg atoms/24.31g mg x 1.74g mg

    = 0.4310 x 10²³mg atoms

    = 4.31 x 10²² mg atoms

B) to find the volume occupied by mg atoms  

    Total volume of cube = 1 cm³

    Volume occupied by mg atoms  

  = 74% of 1cm³

=74/100 x 1cm³= 0.74cm³

To find the volume of 1 mg atom  

4.31 x 10²² mg atoms occupy 0.74 cm³

1 atom will occupy 0.74cm³

1 atom will occupy = 0.74cm³/4.31 x 10²²mg atoms x 1mg atom

volume of 1 mg atom = 0.1716 x 10⁻²²cm²

Volume of 1 mg atom = 4/3 π³ in the form of sphere.

4/3πr³ = 0.1716 x 10⁻²²cm³

R³ = 0.1716 x 10⁻²²cm³x 4/3 x 7/22

R³ = 0.04095 x 10⁻²²cm³

R = 0.1599 x 10⁻⁷cm

1 = 10⁻¹⁰cm

 = 0.1599 x 10⁻⁷cm

 = 1pm/1 x 10⁻¹⁰cm  x 0.1599 x 10-7cm

= 1.599 x 10² pm  

R= 1.6 x 10²pm


3 0
3 years ago
PLEASE HELPP!!!!!!
frosja888 [35]

Answer:

1:144

Step-by-step explanation:

if each floor is 15 feet, the whole building is 60 feet tall. so it does have a scale of 5 inches:60 feet but if you simplify that, its 1 inch: 12 feet, so you convert feet into inches by multiplying by twelve, which gives you a scale of 1:144 inches

3 0
3 years ago
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Definition of segment congruence
postnew [5]

Answer:

Congruent segments are simply line segments that are equal in length. Congruent means equal. Congruent line segments are usually indicated by drawing the same amount of little tic lines in the middle of the segments, perpendicular to the segments

Step-by-step explanation:

8 0
3 years ago
SOLVE AND EXPLAIN! b + m = 400?
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Answer:

b=200 and m=200

Step-by-step explanation:

There are many answers to this problem. You can replace b and n for the number 200. You need to find what two numbers, added up, will give you 400. If b=200 and m=200, when added up, it will give you 400.

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(AP Calc) the graph of the function f shown above has three line segments....
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Answer:

B

Step-by-step explanation:

The average rate of change of f(x) in the closed interval [ a, b ] is

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Here [ a, b ] = [ - 1, 6 ] and from the graph

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f(a) = f(- 1) = 0, thus

average rate of change = \frac{0-0}{6+1} = \frac{0}{7} = 0

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