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
Sphinxa [80]
3 years ago
9

The Fish and Game Department stocked a lake with fish in the following proportions: 30% catfish, 15% bass, 40% bluegill, and 15%

pike. Five years later it sampled the lake to see if the distribution of fish had changed. It found that the 500 fish in the sample were distributed as follows.
Catfish, Bass, Bluegill, pike
112, 95, 210, 83
In the 5-year interval, did the distribution of fish change at the 0.05 level?

1. Find the value of the chi-square statistic for the sample. (Round the expected frequencies to at least three decimal places. Round the test statistic to three decimal places.)
2. Find or estimate the p- value of sample test statistic?
Mathematics
1 answer:
vagabundo [1.1K]3 years ago
5 0

Answer:

1) \chi^2 =\frac{(112-150)^2}{150}+\frac{(95-75)^2}{75}+\frac{(210-200)^2}{200}+\frac{(83-75)^2}{75}=16.313

2) p_v =P(\chi^2_{3}>16.313)=0.000978

And we got the same decision reject the null hypothesis at 5% of significance.

Step-by-step explanation:

Previous concepts

The Chi-Square test of independence is used "to determine if there is a significant relationship between two nominal (categorical) variables". And is defined with the following statistic:

\chi^2 =\sum_{i=1}^n \frac{(O-E)^2}{E}

Where O rpresent the observed values and E the expected values.  

State the null and alternative hypothesis

Null hypothesis: The distribution  is 30% catfish, 15% bass, 40% bluegill, and 15% pike

Alternative hypothesis: The distribution  is NOT 30% catfish, 15% bass, 40% bluegill, and 15% pike

The observed values are given by the table given:

Catfish =112, BAss = 95, Bluegill=210, Pike=83

Calculate the expected values

In order to calculate the expected values we can use the following formula for each cell of the table

E = \% Grand total

E_{Catfish}=500*0.3=150

E_{Bass}=500*0.15=75

E_{Bluegill}=500*0.4=200

E_{Pike}=500*0.15=75

Part 1: Calculate the statistic

\chi^2 =\frac{(112-150)^2}{150}+\frac{(95-75)^2}{75}+\frac{(210-200)^2}{200}+\frac{(83-75)^2}{75}=16.313

\chi^2 =16.313

Calculate the critical value

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

df= (categories-1)=(4-1)= 3

Since the confidence provided is 95% the significance would be \alpha=1-0.95=0.05 and we can find the critical value with the following excel code: "=CHISQ.INV(0.95,3)", and our critical value would be \chi^2_{crit}=7.815

We can calculate also the p value:

p_v =P(\chi^2_{3}>16.313)=0.000978

And we got the same decision reject the null hypothesis at 5% of significance.

You might be interested in
What is 1/6 of 54= 1/3 of WHAT
hodyreva [135]

Answer:

27

Step-by-step explanation:

⅙ × 54 = ⅓ × x

9 = x/3

x = 27

7 0
2 years ago
Read 2 more answers
In a school there are 542 girls and boys. how many pupils are there in that school?
DaniilM [7]

Answer:

There are 1084 pupils in that school.

Step-by-step explanation:

If there are 542 girls and boys then you would have to double 542 to get the total number of people. So, there are 1084 people in that school.

Hope this helps!

6 0
2 years ago
Read 2 more answers
What is the equation for a line passing through (-2,3) and perpendicular to y= -1/2+1 ?
nata0808 [166]

Answer:

y=2x+7

Step-by-step explanation:

<u><em>The correct question is</em></u>

what is the equation for a line passing through (-2,3) and perpendicular to y= -1/2<em>x</em>+1 ?

Remember

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes are equal to -1)

The slope of the given line is m=-1/2

so

the opposite reciprocal is m=2

<em>Find the equation of the line in point slope form</em>

y-y1=m(x-x1)

we have

m=2\\point\ (-2,3)

substitute

y-3=2(x+2)

<em>Convert to slope intercept form</em>

y=mx+b

isolate the variable y

y-3=2x+4

y=2x+4+3

y=2x+7

3 0
3 years ago
Inessa ran 3 laps in 8 minutes. How long would it take her to run 10 laps at this pace? (This is proportions)
Degger [83]

Answer:

26.6 minutes

Step-by-step explanation:

Set up a proportion

3/8 = 10/x

cross multiply

3x = 80

x = 26.6

5 0
3 years ago
Which is an equation of a line that has a slope of -1/3 and passes through the point (-5, 2)?
kramer

Answer:

y= -⅓x +⅓

Step-by-step explanation:

The equation of a line is usually written in the form of y=mx+c, where m is the gradient and c is the y-intercept.

This form is also known as the point-slope form.

Since the slope is given to be -⅓, m= -⅓.

y= -⅓x +c

To find the value of c, substitute a pair of coordinates into the equation.

When x= -5, y=2,

2= -⅓(-5) +c

2 =  \frac{5}{3}  + c \\ c = 2 -  \frac{5}{3}  \\ c =  \frac{1}{3}

Thus, the equation of the line is y= -⅓x +⅓.

7 0
3 years ago
Other questions:
  • Fraction form for -2.3?
    8·2 answers
  • Find the values of x and y.
    14·1 answer
  • (5x² + 8x - 3) + (2x² - 7x + 13x)
    8·2 answers
  • Order the set of numbers from least to greatest: the square root of 64, 8 and 1/7, 8.14 repeating decimal, and 15/2
    12·1 answer
  • Select the two values of x that are roots of this equation
    11·2 answers
  • Hello I need help on Number 9​
    8·1 answer
  • Find the arc length
    5·1 answer
  • Please help!! CORRECT ANSWERS ONLY! Please show your work!
    14·2 answers
  • HELP ME PLS!!! This is important
    7·2 answers
  • Is ac perpidicular to xz? explain
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!