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Evgen [1.6K]
2 years ago
7

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

e 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 the mean difference d bar = 3.125, sd = 2.911, and n = 8, and that you wish to test the following hypothesis at the 10% level of significance: H0 : µd = 0 against H1 : µd > 0.
What decision rule would you use? Group of answer choices

a).Reflect H0 if the test statistic is greater than -1.895 and less than 1.896.

b). Reject H0 if test statistic is greater than -1.895.

c). Reject H0 if test statistic is greater than 1.895.

d). Reject H0 if test statistic is less than 1.895
Mathematics
1 answer:
Olegator [25]2 years ago
4 0

Answer:

The critical value for this case can be calculated using the t distribution with 7 degrees of freedom and the critical value would be a value who accumulates 0.1 of the area in the right of the distribution and the best decision based on the possible options would be:

c). Reject H0 if test statistic is greater than 1.895.

Step-by-step explanation:

The system of hypothesis for this case are:

Null hypothesis: \mu_d = 0

Alternative hypothesis: \mu_d >0

The statistic for this case is given by:

t=\frac{\bar d -0}{\frac{s_d}{\sqrt{n}}}=\frac{3.125 -0}{\frac{2.911}{\sqrt{8}}}=3.04

The degrees of freedom are given by:

df=n-1=8-1=7

The p value for this case can be calculated from this probability:

p_v =P(t_{(7)}>3.4) =0.0057

The critical value for this case can be calculated using the t distribution with 7 degrees of freedom and the critical value would be a value who accumulates 0.1 of the area in the right of the distribution and the best decision based on the possible options would be:

c). Reject H0 if test statistic is greater than 1.895.

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Leno4ka [110]

Answer:

\sqrt{55}

Step-by-step explanation:

Based off of what we do know, if we can find length DB we can use the pythagorous theorem (I will be assigning the variable z)

x^{2} =36+z^{2} \\\\y^{2}=25+z^2\\\\x^{2} +y^2=121\\\\

First equation is for triangle ABD

Second is for BCD

And the last one is for ACD

Substitute x^{2} and y^2

36+z^2+25+z^2=121\\\\61+2z^2=121\\\\2z^2=60\\\\z^2=30\\\\z=\sqrt{30}

As discovered before

y^2=25+z^2\\\\y^2=25+30\\\\y^2=55\\\\y=\sqrt{55}

8 0
3 years ago
Hhellp pwease I want to know what's wrong and right
Studentka2010 [4]

Answer:

A: False

B: False

C: True

D: True

E: False

F: True

G: True

H: True

Step-by-step explanation:

A: 9(x - 2) = 9x + 2

9x - 18 = 9x + 2 FALSE

B: 65 - y = y - 65

(equation rearranged) -y + 65 = y - 65 FALSE

C: g (times) h = h (times) g     (TRUE due to the commutative property of multiplication)

D: a (times) 0 = 0      (TRUE because anything times 0 equals 0)

E: (4 (times) 2) - r = 4 (2 (times) r)

8 - r =  8 - 4r FALSE

F: k + 0 = k TRUE

G: (a + x) + y = a + (x + y)

a + x + y = a + x + y TRUE

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2 years ago
Lim x-1 x³-2x²+3x-2/(2x^4-3x+1)
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Since the limit becomes the undetermined form

\displaystyle \lim_{x\to 1} \dfrac{x^3-2x^2+3x-2}{2x^4-3x+1} \to \dfrac{0}{0}

it means that both polynomials have a root at x=1. So, we can fact both numerator and denominator:

x^3-2x^2+3x-2 = (x-1)(x^2-x+2)

2x^4-3x+1 = (x-1)(2x^3+2x^2+2x-1)

So, the fraction becomes

\dfrac{(x-1)(x^2-x+2)}{(x-1)(2x^3+2x^2+2x-1)} = \dfrac{x^2-x+2}{2x^3+2x^2+2x-1}

Now, as x approaches 1, you have no problems anymore:

\displaystyle \lim_{x\to 1} \dfrac{x^2-x+2}{2x^3+2x^2+2x-1} \to \dfrac{2}{5}

4 0
3 years ago
Johnny says that rolling a number cube twice and getting a 6 both times is an example of dependent events because getting a 6 on
hjlf

Answer:

This is not correct

Step-by-step explanation:

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8 0
2 years ago
Read 2 more answers
For each pair of points below, think about the line that joins them. For which pairs is the line parallel to the y-axis? Circle
gogolik [260]

Answer:

Option B.

Step-by-step explanation:

If two lines are parallel then their slopes are always same.

Following this rule we can find the slope by the given pairs of coordinates of the options.

If the slope of the line is same as the slope of y axis then the line passing through these points will be parallel to the y axis.

Slope of y - axis = ∞

Option A). Slope = \frac{y-y'}{x-x'}

                            =  \frac{24-8.5}{3.22-3.2}

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Therefore, line passing through points (3.2, 8.5) and (3.22, 24) is not parallel to y axis.

Option B). Slope of the line passing through (\frac{40}{3},\frac{14}{3}) and (\frac{40}{3},7) will be

= \frac{\frac{14}{3}-7}{\frac{40}{3}-\frac{40}{3}}

= ∞

Therefore, line passing though these points is parallel to the y axis.

Option C). Slope of the line passing through (2.9,5.4) and (7.2, 5.4)

= \frac{5.4-5.4}{7.2-2.9}

= 0

Therefore, slope of this line is not equal to the slope of y axis.

Option B. is the answer.

5 0
3 years ago
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