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
TiliK225 [7]
3 years ago
5

Find the p-value: An independent random sample is selected from an approximately normal population with an unknown standard devi

ation. Find the p-value for the given set of hypotheses and T test statistic. Also determine if the null hypothesis would be rejected at alpha = 0.05(a) HA : u > u0, N = 11, T = 1 :91(b) HA: < u0, N = 17, T = -3:45(c) HA: u ? u0 , N = 7, T = 0.83(d) HA: u > u0 , N = 28, T = 2.13

Mathematics
1 answer:
vladimir1956 [14]3 years ago
5 0

Answer:

(a) <em>p</em>-value = 0.043. Null hypothesis is rejected.

(b) <em>p</em>-value = 0.001. Null hypothesis is rejected.

(c) <em>p</em>-value = 0.444. Null hypothesis is not rejected.

(d) <em>p</em>-value = 0.022. Null hypothesis is rejected.

Step-by-step explanation:

To test for the significance of the population mean from a Normal population with unknown population standard deviation a <em>t</em>-test for single mean is used.

The significance level for the test is <em>α</em> = 0.05.

The decision rule is:

If the <em>p - </em>value is less than the significance level then the null hypothesis will be rejected. And if the <em>p</em>-value is more than the value of <em>α</em> then the null hypothesis will not be rejected.

(a)

The alternate hypothesis is:

<em>Hₐ</em>: <em>μ</em> > <em>μ₀</em>

The sample size is, <em>n</em> = 11.

The test statistic value is, <em>t</em> = 1.91 ≈ 1.90.

The degrees of freedom is, (<em>n</em> - 1) = 11 - 1 = 10.

Use a <em>t</em>-table t compute the <em>p</em>-value.

For the test statistic value of 1.90 and degrees of freedom 10 the <em>p</em>-value is:

The <em>p</em>-value is:

P (t₁₀ > 1.91) = 0.043.

The <em>p</em>-value = 0.043 < <em>α</em> = 0.05.

The null hypothesis is rejected at 5% level of significance.

(b)

The alternate hypothesis is:

<em>Hₐ</em>: <em>μ</em> < <em>μ₀</em>

The sample size is, <em>n</em> = 17.

The test statistic value is, <em>t</em> = -3.45 ≈ 3.50.

The degrees of freedom is, (<em>n</em> - 1) = 17 - 1 = 16.

Use a <em>t</em>-table t compute the <em>p</em>-value.

For the test statistic value of -3.50 and degrees of freedom 16 the <em>p</em>-value is:

The <em>p</em>-value is:

P (t₁₆ < -3.50) = P (t₁₆ > 3.50) = 0.001.

The <em>p</em>-value = 0.001 < <em>α</em> = 0.05.

The null hypothesis is rejected at 5% level of significance.

(c)

The alternate hypothesis is:

<em>Hₐ</em>: <em>μ</em> ≠ <em>μ₀</em>

The sample size is, <em>n</em> = 7.

The test statistic value is, <em>t</em> = 0.83 ≈ 0.82.

The degrees of freedom is, (<em>n</em> - 1) = 7 - 1 = 6.

Use a <em>t</em>-table t compute the <em>p</em>-value.

For the test statistic value of 0.82 and degrees of freedom 6 the <em>p</em>-value is:

The <em>p</em>-value is:

P (t₆ < -0.82) + P (t₆ > 0.82) = 2 P (t₆ > 0.82) = 0.444.

The <em>p</em>-value = 0.444 > <em>α</em> = 0.05.

The null hypothesis is not rejected at 5% level of significance.

(d)

The alternate hypothesis is:

<em>Hₐ</em>: <em>μ</em> > <em>μ₀</em>

The sample size is, <em>n</em> = 28.

The test statistic value is, <em>t</em> = 2.13 ≈ 2.12.

The degrees of freedom is, (<em>n</em> - 1) = 28 - 1 = 27.

Use a <em>t</em>-table t compute the <em>p</em>-value.

For the test statistic value of 0.82 and degrees of freedom 6 the <em>p</em>-value is:

The <em>p</em>-value is:

P (t₂₇ > 2.12) = 0.022.

The <em>p</em>-value = 0.444 > <em>α</em> = 0.05.

The null hypothesis is rejected at 5% level of significance.

You might be interested in
How many miles did Brian run?
VashaNatasha [74]

Answer:

5.28 miles

Step-by-step explanation:

he ran a total of 18 days. 95 miles dived by 18 days is 5.27 if you round it its 5.28

4 0
3 years ago
Read 2 more answers
Sanji paid 25 for two scarves which were different prices when she got home she could not find the receipt she remember that one
laila [671]
Answer:

The answer is x = 14 the more expensive scarf

Step-by-step explanation:

x + y = 25

3 + y + y = 25 (x = 3 + y)

3 + 2y = 25

2y = 25 - 3

2y = 22

y = 22/2

y = 11

x = 3 + y

x = 3 + 11

x = 14 (the more expensive scarf)

(x,y) ; (14,11)
5 0
3 years ago
If X =4 in., find the area of the trapezoid in problem 22
Digiron [165]

Answer:

Need a picture of the problem.

Step-by-step explanation:

5 0
2 years ago
Bartolo is running a race. He determines that if he runs at an average speed of 15 feet/second, he can finish the race in 6 seco
Gelneren [198K]

Answer:

C

Step-by-step explanation:

the distance is 15•6 = 18•5 = 90 feet

so, time needed = 90/30 = 3 second

7 0
3 years ago
For babysitting, Nicole charges a flat fee of $3, plus $5 per hour. Write an equation for the cost, C, after h hours of babysitt
Alexeev081 [22]
C = 5h + 3
C = 5(5) + 3
She will make $28
4 0
3 years ago
Other questions:
  • Help, can’t figure it out, need help fast
    8·1 answer
  • If a/x + 1 = c/x which is an expression for x terms in terms of c and a?
    6·1 answer
  • suppose you have a rectangle with a length 8 cm and width 3 cm. Now suppose the sides are doubled. Find the percent os increase
    7·1 answer
  • What is the equation of a line through the points (0, 9) and (3, 0)?
    12·2 answers
  • The memory card on Madison's digital camera can
    9·1 answer
  • In a square with side length of 6, what is the distance between the center of the square and the center of the largest equilater
    6·1 answer
  • A company makes Citi bikes. 95% (i.e., 0.95) pass final inspection. Suppose that 5 bikes are randomly selected.
    12·1 answer
  • PLEASE HELP THIS IS DUE TODAY EXPLAIN IF YOU CAN OR EXPLAIN IF YOU WANT.
    10·2 answers
  • Question 6
    6·1 answer
  • Please help me I have gone over the tutorial 3 times and I cant figure it out pleaaase help me i will love you forever​
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!