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Consider the following hypothesis test. H0: μ ≥ 55 Ha: μ < 55 A sample of 36 is used. Identify the p-value and state your con

Ket [755]

Answer:

Step-by-step explanation:

Given that:

$H_o: \mu \ge 55 \ \\ \\ H_1 : \mu < 55$

(a) For x = 54 and s = 5.3

The test statistics can be computed as:

$Z = \dfrac{\overline x - \mu}{\dfrac{s}{\sqrt{n}} }$

$Z = \dfrac{54-55}{\dfrac{5.3}{\sqrt{36}} }$

$Z = \dfrac{-1}{\dfrac{5.3}{6} }$

Z = -1.132

degree of freedom = n - 1

= 36 - 1

= 35

Using the Excel Formula:

P-Value = T.DIST(-1.132,35,1) = 0.1326

Decision: p-value is greater than significance level; do not reject $\mathbf{H_o}$

$Conclusion: \ There \ is \ insufficient \ evidence \ to \ conclude \ that \$ $\mu < 55$

b

For x = 53 and s = 4.6

The test statistics can be computed as:

$Z = \dfrac{\overline x - \mu}{\dfrac{s}{\sqrt{n}} }$

$Z = \dfrac{53-55}{\dfrac{4.6}{\sqrt{36}} }$

$Z = \dfrac{-2}{\dfrac{4.6}{6} }$

Z = -2.6087

degree of freedom = n - 1

= 36 - 1

= 35

Using the Excel Formula:

P-Value = T.DIST(-2.6087,35,1) =0.0066

Decision: p-value is < significance level; we reject the null hypothesis.

$Conclusion: \ There \ is \ sufficient \ evidence \ to \ conclude \ that$ $\mu < 55$

c)

For x = 56 and s = 5.0

The test statistics can be computed as:

$Z = \dfrac{\overline x - \mu}{\dfrac{s}{\sqrt{n}} }$

$Z = \dfrac{56-55}{\dfrac{5.0}{\sqrt{36}} }$

Z = 1.2

degree of freedom = n - 1

= 36 - 1

= 35

Using the Excel Formula:

P-Value = T.DIST(1.2,35,1) = 0.88009

Decision: p-value is greater than significance level; do not reject $\mathbf{H_o}$

$Conclusion: \ There \ is \ insufficient \ evidence \ to \ conclude \ that \$ $\mu < 55$

6 0

3 years ago

Two trains leave the station at the same, one heading west and the other east. The westbound train travels at 55 miles per hour.

Mars2501 [29]

The time that taken for the two trains is 1.2 hours.

The computation of the time taken for the two trains is shown below:

Given that

The westbound train travels 55 miles per hour.

And, the eastbound train travels 75 miles per hour.

So, the total speed is

= 55 miles per hour + 75 miles per hour

= 130 miles per hour

The distance is 156 miles

So, the time taken is

$= \frac{distance}{speed}\\\\= \frac{156\ miles}{130\ miles\ per\ hour}\\\\$

= 1.2 hours

Therefore we can conclude that the time that taken for the two trains is 1.2 hours.

Learn more about the speed here: brainly.com/question/21791162

4 0

3 years ago

Read 2 more answers

Identify the sine function with the given attributes.

Thepotemich [5.8K]

Answer:

<em>Last option </em>

$f(t)=sin(\pi(t -3)) + 4$

Step-by-step explanation:

The general sine function has the following form

$y = Asin(bt-\phi) + k$

Where A is the amplitude: half the vertical distance between the highest peak and the lowest peak of the wave.

$\frac{2\pi}{b}$ is the period: time it takes the wave to complete a cycle.

k is the vertical displacement.

$\phi$ phase shift

We know that:

amplitude: 1; period: 2; phase shift: 3; vertical shift: 4

Thus:

$A =1$

$\frac{2\pi}{b}=2$

$b=\pi$

$\phi=3$

$k=4$

Then the function is:

$f(t)=sin(\pi(t -3)) + 4$

The answer is last option

4 0

3 years ago

If 3x^2+3y^2=42 and xy =-15.Find the value (x-y)^2

Alexxandr [17]

Answer:

44

Step-by-step explanation:

Given, 3x^2 + 3y^2 = 42

=>3(x^2 + y^2) = 42 =>x^2 + y^2 = 42/3= 14

Thus,

= (x - y)^2

= x^2 + y^2 - 2xy

= (x^2 + y^2) - 2xy

= 14 - 2(-15)

= 14 + 30

= 44

4 0

3 years ago

What is the remainder of x^5+2x^4+9x^3-6x^2+3x+3165 divided by x-5

riadik2000 [5.3K]

Answer:

8530

Step-by-step explanation:

The remainder is 5⁵ + 2(5)⁴ + 9(5)³ - 6(5)² + 3(5) + 3165 = 8530

4 0

2 years ago