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
Natali5045456 [20]
1 year ago
12

Assume that a simple random sample has been selected from a normally distributed population. State the hypotheses, find the test

statistic, critical value(s) , P-value , and state the final conclusion.Test the claim that for the population of female college students, the mean weight is given by μ = 132 lb. Sample data are summarized as n = 20, overbar(x) = 137 lb, and s = 14.2 lb. Use a significance level of α = 0.1.
Mathematics
1 answer:
BaLLatris [955]1 year ago
7 0

Solution

Hypotheses:

- The population mean is 132. In order to test the claim that the mean is 132, we should check for if the mean is not 132.

- Thus, the Hypotheses are:

\begin{gathered} H_0:\mu=132 \\ H_1:\mu\ne132 \end{gathered}

Test statistic:

- The test statistic has to be a t-statistic because the sample size (n) is less than 30.

- The formula for finding the t-statistic is:

\begin{gathered} t=\frac{\bar{X}-\mu}{\frac{s}{\sqrt{n}}} \\  \\ where, \\ \bar{X}=\text{ Sample mean} \\ \mu=\text{ Population mean} \\ s=\text{ Standard deviation} \\ n=\text{ Sample size} \end{gathered}

- Applying the formula, we have:

\begin{gathered} t=\frac{137-132}{\frac{14.2}{\sqrt{20}}} \\  \\ t=\frac{5}{3.1752} \\  \\ t\approx1.5747 \end{gathered}

Critical value:

- The critical value t-critical, is gotten by reading off the t-distribution table.

- For this, we need the degrees of freedom (df) which is gotten by the formula:

\begin{gathered} df=n-1 \\ df=20-1=19 \end{gathered}

- And then we also use the significance level of 0.1 and the fact that it is a two-tailed test to trace out the t-critical. (Note: significance level of 0.1 implies 10% significance level)

- This is done below:

- The critical value is 1.729

P-value:

- To find the p-value, we simply check the table for where the t-statistic falls.

- The t-statistic given is 1.5747. We simply check which values this falls between in the t-distribution table. It falls between 1.328 and 1.729. We can simply choose a value between 0.1 and 0.05 and multiply the result by 2 since it is a two-tailed test.

- However, we can also use a t-distribution calculator, we have:

- Thus, the p-value is 0.13183

Final Conclusion:

- The p-value is 0.13183, and comparing this to the significance level of 0.1, we can see that 0.13183 is outside the rejection region.

- Thus, the result is not significant and we fail to reject the null hypothesis

You might be interested in
Solve the following equation. Then place the correct number in the box provided. 6x - 8 = 16
uysha [10]
6x-8=16
6x-8+8=16+8
6x=24
6x=24
— —
6 6
X= 4
8 0
3 years ago
Read 2 more answers
The mode is the
taurus [48]

Answer:

most common, 4, c, 9

Step-by-step explanation:

6 0
2 years ago
Read 2 more answers
Please help ASAP!!!!!
ra1l [238]
These tables have infinitely many values, but the simplest ones would be:
a) x|y
    3|5
    6|10
    9|15

b) x|y
    2|1
    4|2
    6|3

Your graph for c would look like the attached picture

7 0
3 years ago
Read 2 more answers
Which number is a solution of the inequality 8 - 1/4 b > 27
Brrunno [24]

The inequality is 8-1/4x>27. The solution of the inequality is b<-76.

Given that,

The inequality is 8-1/4x>27

We must determine how to address the inequity.

Take,

8-1/4x>27

Multiply the inequality's two sides by its lowest common denominator,

4×8-4×1/4b>27×4

Reduce the expression to the lowers term,

4×8-b>4×27

Calculate the product or quotient,

32-b>4×27

Calculate the product or quotient,

32-b>108

Rearrange unknown terms to the left side of the equation,

-b>108-32

Calculate the sum or difference,

-b>76

Divide the inequality's two sides by the variable's coefficient,

b<-76

Therefore, the solution of the inequality is b<-76.

To learn more about inequality visit: brainly.com/question/28823603

#SPJ1

6 0
11 months ago
8x=4x^2-1 <br>solve by completing the square
Klio2033 [76]
Get the x terms by themselves on one side and a constant on the other side of the equal sign...

4x^2-8x=1  make the leading coefficient equal to one...

x^2-2x=1/4  now halve the linear coefficient, -2 in this case, square it, and add that value to both sides of the equation...-2/2=-1, -1^2=1 so

x^2-2x+1=1+1/4

x^2-2x+1=5/4  now the left side is a perfect square...

(x-1)^2=5/4  take the square root of both sides...

x-1=±√(5/4)  add 1 to both sides

x=1±√(5/4)
7 0
3 years ago
Read 2 more answers
Other questions:
  • Which situation could this diagram represent
    15·2 answers
  • How much water should be added to 3 gallons of pure acid in order to obtain the 15% acid solution? plz help due tommorow mornimi
    14·1 answer
  • Sara wants to find the input value that produces the same output for the functions represented by the tables.
    13·2 answers
  • Mrs. Bea’s Bakery offers a Saturday morning special where your entire meal is 15% off. How much will a $32.00 meal cost after th
    14·2 answers
  • A model of the is 2.9 ft tall and 1.2 ft wide. The Eiffel Tower is actually 410 ft wide. What is the actual height of the Eiffel
    6·1 answer
  • Which does NOT represent a constant rate of change of 70 miles per hour for a car? Question 4 options: The car travels 245 miles
    5·2 answers
  • What is 31 1/4 × 112
    9·1 answer
  • Find the measure of angle b
    15·2 answers
  • Solve. 7/3x+1/3x=4+5/3x The value of x is
    7·2 answers
  • In the past month, Lisa rented 7 video games and 1 DVD. The rental price for each video game was $2.30. The rental price for the
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!