1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
otez555 [7]
3 years ago
10

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

clusion for each of the following sample results. Use α = 0.01.
(a) x = 54 and s = 5.3 Find the value of the test statistic. (Round your answer to three decimal places.)
Find the p-value. (Round your answer to four decimal places.)
State your conclusion.
(b) x = 53 and s = 4.6
Find the value of the test statistic. (Round your answer to three decimal places.)
Find the p-value. (Round your answer to four decimal places.)
p-value =
(c) x = 56 and s = 5.0
Find the value of the test statistic.
Find the p-value. (Round your answer to four decimal places.)
p-value =
State your conclusion.
Mathematics
1 answer:
Ket [755]3 years ago
6 0

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 = \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

You might be interested in
Pls help me i need help 10 pt
Nataly [62]
Fret seems like the best option. 
5 0
3 years ago
Read 2 more answers
I WILL GIVE BRAINLIEST!!!
MrMuchimi

Answer:

Answer is after 20 miles

Step-by-step explanation:

10 +2.5x = 3x

10 = 3x-2.5x

10=0.5x

10/.5=x

x=20

At 20 miles they both have a cost of 60

4 0
2 years ago
Read 2 more answers
Consider the following statement. If r is any rational number and s is any irrational number, then r s is irrational. (a) Which
olganol [36]

Answer:

(a) If r is any rational number and s is any irrational number, then r/s is rational

(b) The statement is false when r is 0

Step-by-step explanation:

Given

r \to rational number

s \to irrational number

\frac{r}{s} \to irrational number

Solving (a): The negation

To get the negation of a statement, we only need to negate the end result

In other words, the number type of r and s will remain the same, but r/s will be negated.

So, the negation is:

r \to rational number

s \to irrational number

\frac{r}{s} \to rational number

Solving (b): When r/s is irrational is false

Given that:

\frac{r}{s} \to irrational number

Set r to 0

So:

\frac{r}{s} = \frac{0}{s}

\frac{r}{s} = 0 -- rational

<em>Hence, the statement is false when r is 0</em>

8 0
2 years ago
Miss Wilson has spent $6 on breakfast using her debit card 5 mornings per week for the past 8 weeks. What is the change in Miss
Lera25 [3.4K]

Answer:

(6x5) • 8

Step-by-step explanation:

We’ll I find it’s 6 dollars a day and their are 5 days that would be 30 but this went in for 8 weeks so it would be 30 x 8 which equal 240

8 0
3 years ago
Read 2 more answers
HELP PLEASE. A pizza shop charges customers based on the area of the pizza they order. The cost of a pizza in dollars can be rep
san4es73 [151]

For this case we have that the cost of each pizza is given by the following function:

S (r) = 0.1 \pi * r ^ 2

Where:

r: It's the radius of the pizza

IF a pizza cost $26.32 we have:

26.32 = 0.1 \pi * r ^ 2

We cleared the radius, using \pi = 3.14:

\frac {26.32} {0.1} = \pi * r ^ 2\\263.2 = 3.14r ^ 2\\\frac {263.2} {3.14} = r ^ 2\\83.82 = r ^ 2\\r = \pm \sqrt {83.82}

We choose the positive value:

r = 9.15

So, the radius of the pizza is 9.16 \ in

Then, the diameter is: 2r = 2 * 9.15 = 18.30 \ in

Finally, the diameter of the pizza is:18.30 \ in

Answer:

Option B

4 0
3 years ago
Read 2 more answers
Other questions:
  • the distance around the outside of cedar park is 0.8 mile. Joanie ran 0.25 of the distance during her lunch break. How far did s
    5·1 answer
  • A regular pentagon and a rectangle have the same perimeter. The width of the rectangle is 10 more than its length. The length of
    8·1 answer
  • Lines p and q are parallel.
    15·1 answer
  • Which expression is 444 times as large as the expression 34 -15
    15·1 answer
  • The hour hand of a clock moves -30° every hour. How many degrees does it move in 2 1/5 hours?
    13·1 answer
  • Write an equation that will give the equation y=5 when x=12
    14·1 answer
  • A standard fire hose is 50 feet long. What is the length of the hose in yards and feet?
    8·2 answers
  • Can someone help me
    5·2 answers
  • Electric utility poles in the form of right cylinders are made out of wood that costs $25.46 per cubic foot. Calculate the cost
    5·1 answer
  • a vendor is thinking about changing the number of sweatshirts he brings to tan event. to make sure he doesn't run out, he plans
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!