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
Maksim231197 [3]
3 years ago
15

According to the norms established for a reading comprehension test, eighth-graders should average 83.2 with a standard deviatio

n of 8.6. If 45 randomly selected eighth graders from a certain school district averaged 86.7 with a standard deviation of 8.6, test the null hypothesis LaTeX: \muμ= 83.2 against the alternative hypothesis LaTeX: \muμ> 83.2 at the .01 level of significance. And then decide whether there is evidence to support the superintendent's claim that her eighth graders are above average.
Mathematics
1 answer:
joja [24]3 years ago
8 0

Answer:

t=\frac{86.7-83.2}{\frac{8.6}{\sqrt{45}}}=2.73    

p_v =P(t_{44}>2.73)=0.0045    

If we compare the p value and a significance level given \alpha=0.01 we see that p_v so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the population mean is signficantly higher than 83.2 at 1% of significance.

Step-by-step explanation:

Data given and notation    

\bar X=86.7 represent the average life for the sample    

s=8.6 represent the population standard deviation    

n=45 sample size    

\mu_o =83.2 represent the value that we want to test    

\alpha=0.01 represent the significance level for the hypothesis test.    

t would represent the statistic (variable of interest)    

p_v represent the p value for the test (variable of interest)    

State the null and alternative hypotheses.    

We need to apply a two tailed  test.  

What are H0 and Ha for this study?    

Null hypothesis:  \mu \leq 83.2  

Alternative hypothesis :\mu > 83.2  

Compute the test statistic  

The statistic for this case is given by:  

t=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}} (1)    

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".    

Calculate the statistic    

We can replace in formula (1) the info given like this:    

t=\frac{86.7-83.2}{\frac{8.6}{\sqrt{45}}}=2.73    

Give the appropriate conclusion for the test  

First we need to calculate the degrees of freedom given by:

df=n-1=45-1=44

Since is a one side right tailed test the p value would be:    

p_v =P(t_{44}>2.73)=0.0045    

Conclusion    

If we compare the p value and a significance level given \alpha=0.01 we see that p_v so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the population mean is signficantly higher than 83.2 at 1% of significance.

You might be interested in
What are the numerical measures of each angle in the diagram? 1 and 3 measure degrees. 2 and 4 measure degrees. (3x - 1)º (2x +
Tanya [424]

Answer:

Step-by-step explanation:

In the diagram shown, the measure of angle 1 is oppositely directed to angle 2 and oppositely directed angles are equal.

Hence <1 = <3

Given < 1 = 3x-1 and <3 = 2x+9

Hence 3x-1 =  2x+9

collect like terms

3x-2x = 9+1

x = 10°

Since <1 = 3x-1

on substituting x = 10

<1 = 3(10)-1

<1 = 30-1

<1 = 29°

<1+<2 = 180 (angle on a straight line)

29+<2 = 180

<2 = 180-29

<2 = 151°

Similarly, on substituting x = 10 into <3

<3 = 2x+9

<3 = 2(10)+9

<3 = 20+9

<3 = 29°

<3+<4 = 180 (angle on a straight line)

29+<4 = 180

<4 = 180-29

<4 = 151°

3 0
3 years ago
Read 2 more answers
Tim Worker expects Social Security benefits of $937 per month. His wife, Mary, is eligible for a wife's benefit of 50 percent of
serg [7]

Answer:

The answer is B: 468.50

Step-by-step explanation:


6 0
3 years ago
Read 2 more answers
Find the measure of angle 3​
OlgaM077 [116]

Answer:

The measure of angle 3 is 42

8 0
3 years ago
Which expression is equivalent to 1/2x+(−7)−2 1/4x−(−2
Lynna [10]

The equivalent expression to the given expression is \mathbf{=-(\dfrac{7}{4}x+5)}

<h3>What is an algebraic expression?</h3>

Algebraic expressions are mathematical expressions. They usually consist of one or more variables with their coefficients and arithmetic operators such as: (division, multiplication, addition, and subtraction).

From the given expression, we are to determine an expression that is equivalent to:

=\dfrac{1}{2}x + (-7) -2 \dfrac{1}{4}x -(-2)

To do this, we are going to simplify the above-given expression to its lowest term since we are not given any options to choose equivalent expressions from.

By doing so, we have:

=\dfrac{1}{2}x -7 -\dfrac{9}{4}x +2

=\dfrac{1}{2}x -\dfrac{9}{4}x +2 -7

=\dfrac{1}{2}x -\dfrac{9}{4}x -5

=-\dfrac{7}{4}x-5

\mathbf{=-(\dfrac{7}{4}x+5)}

Learn more about solving algebraic expressions here:

brainly.com/question/4344214

#SPJ1

5 0
2 years ago
What number would be added to both sides in order to complete the square when solving x^2+8x=9?
Margaret [11]
You can figure this out if you just look at (x+a)^2 = x^2 + 2ax + a^2. See, the constant term, a^2, is the coefficient of x (2a), divided by 2 (2a/2=a), and then squared (a^2) 

<span>So you equation has 8x. 8/2 = 4, and 4^2 = 16. So the answer is A.</span>
7 0
3 years ago
Read 2 more answers
Other questions:
  • How is a rational number converted to its decimal form?
    7·2 answers
  • Explain why it works to break apart a number by place values to multiply
    15·2 answers
  • Sally has a discount card that reduces the price of her grocery bill in a certain grocery store by 5%. if c represents the cost
    8·1 answer
  • The graph of the piecewise function is shown.
    10·2 answers
  • Find the sum of the polynomials.
    12·1 answer
  • How do you find the volume, in cubic inches of a prism?
    10·1 answer
  • The Sommers invested $5000 for three years at 6.5%. How much interest did the investment earn in three years? What was the total
    11·1 answer
  • A driver works 40 hours a week for the first two months on the job. How much more per week does the driver make after 28 days?
    11·1 answer
  • 12x+6n-36 in standard form
    13·1 answer
  • Each interior angle of a regular polygon is 140°.Find the number of sides​
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!