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Keith_Richards [23]
3 years ago
11

Determine the decision criterion for rejecting the null hypothesis in the given hypothesis​ test; i.e., describe the values of t

he test statistic that would result in rejection of the null hypothesis. We wish to compare the means of two populations using paired observations. Suppose that d overbar equals​3.125, subscript dequals​2.911, and nequals​8, and that you wish to test the following hypothesis at the​ 10% level of significance. H0​: mu Subscript d equals 0 against H1​: muSubscript dgreater than0 What decision rule would you​ use?
Mathematics
1 answer:
slega [8]3 years ago
7 0

Answer:

t = \frac{3.125-0}{\frac{2.911}{\sqrt{8}}}= 3.036

We can use the p value as a decision rule is p_v we reject the null hypothesis.

Now we can find the degrees of freedom given by:

df = n-1=8-1=7

And the p value would be:

p_v = P(t_{7} >3.036) = 0.0094

And since the p_v we have enough evidence to reject the null hypothesis in favor to the alternative hypothesis.

Step-by-step explanation:

For this case we have the following statistics for the difference between the paired observations:

\bar d = 3.125 the sample mean for the paired difference

s_d = 2.911 the sample deviation for the paired difference data

n =8 the sample size

The system of hypothesis that we want to check is:

Null hypothesis: \mu_d =0

Alternative hypothesis: \mu_d > 0

And the statistic is given by:

t = \frac{\bar d -\mu_d}{\frac{s_d}{\sqrt{n}}}

And replacing we got:

t = \frac{3.125-0}{\frac{2.911}{\sqrt{8}}}= 3.036

We can use the p value as a decision rule is p_v we reject the null hypothesis.

Now we can find the degrees of freedom given by:

df = n-1=8-1=7

And the p value would be:

p_v = P(t_{7} >3.036) = 0.0094

And since the p_v we have enough evidence to reject the null hypothesis in favor to the alternative hypothesis.

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Solve the following triangle. Given A=51 degrees b=40 c=45
STALIN [3.7K]

Answer:

a=36.87\ units

B=57.47^o

C=71.53^o

Step-by-step explanation:

step 1

Find the length side a

Applying the law of cosines

a^2=b^2+c^2-2(b)(c)cos(A)

substitute the given values

a^2=40^2+45^2-2(40)(45)cos(51^o)

a^2=1,359.4466

a=36.87\ units

step 2

Find the measure of angle B

Applying the law of sines

\frac{a}{sin(A)} =\frac{b}{sin(B)}

substitute the given values

\frac{36.87}{sin(51^o)} =\frac{40}{sin(B)}

sin(B)=\frac{sin(51^o)}{36.87}{40}

B=sin^{-1}(\frac{sin(51^o)}{36.87}{40})=57.47^o

step 3

Find the measure of angle C

Remember that the sum of the interior angles in any triangle must be equal to 180 degrees

so

A+B+C=180^o

substitute the given values

51^o+57.47^o+C=180^o

108.47^o+C=180^o

C=180^o-108.47^o=71.53^o

5 0
3 years ago
If total employee benefits are calculated as a percentage of their gross pay, which of the following employees receives the larg
vlabodo [156]

Consider all employees.

A.

  • gross pay $32,600 - 100%,
  • total job benefits $33,600 - x%.

Then

\dfrac{32,600}{33,600}=\dfrac{100}{x},\\ \\32,600\cdot x=33,600\cdot 100,\\ \\x=\dfrac{33,600\cdot 100}{32,600}=\dfrac{33,600}{326} \approx 103.07.

Employee A receives 3.07% of gross pay in employee benefits.

B.

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  • total job benefits $34,000 - x%.

Then

\dfrac{32,900}{34,000}=\dfrac{100}{x},\\ \\32,900\cdot x=34,000\cdot 100,\\ \\x=\dfrac{34,000\cdot 100}{32,900}=\dfrac{34,000}{329} \approx 103.34.

Employee B receives 3.34% of gross pay in employee benefits.

C.

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Then

\dfrac{33,400}{33,900}=\dfrac{100}{x},\\ \\33,400\cdot x=33,900\cdot 100,\\ \\x=\dfrac{33,900\cdot 100}{33,400}=\dfrac{33,900}{334} \approx 101.50.

Employee C receives 1.50% of gross pay in employee benefits.

D.

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Then

\dfrac{33,700}{34,700}=\dfrac{100}{x},\\ \\33,700\cdot x=34,700\cdot 100,\\ \\x=\dfrac{34,700\cdot 100}{33,700}=\dfrac{34,700}{337} \approx 102.97.

Employee D receives 2.97% of gross pay in employee benefits.

Answer: correct choice is B.

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Answer:

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Step-by-step explanation:

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