A rare type of heredity change causes the bacterium in E. coli to become resistant to the drug strepto- mycin. This type of change, called mutation, can be detected by plating many bacteria on petri dishes containing an antibiotic medium. Any colonies that grow on this medium result from a single mutant cell. A sample of n 200 petri dishes of streptomycin agar were each plated with 106 bacteria, and the numbers of colonies were counted on each dish. The observed results were that 110 dishes had 0 colonies, 61 had 1, 17 had 2, 9 had 3, 3 dishes had 4 colonies, and no dishes had more than 4 colonies. Let X equal the number of colonies per dish. Test the hypothesis that X has a Poisson distribution. (a) Compute i as an estimate of λ. (b) Set up classes (categories) for the a-values so that the expected number of observations in each class is at least 5 (using z as an estimate of λ) (c) Using the classes from (b), compute the test statistic and give the critical region at a = 0.01

Answers

Answer 1

(a) The sample mean can be used as an estimate of λ: 0.95.

(b) The expected number of observations in each class are

Class 0: 18.2

Class 1: 86.5

Class 2: 163.8

Class 3 or more:  31.5

(c) The distribution of X is not Poisson because we reject the null hypothesis that X has a Poisson distribution with parameter λ = 0.95.

(a) The sample mean can be used as an estimate of λ:

i = (110×0 + 61×1 + 17×2 + 9×3 + 3×4) / 200 = 0.95

(b) We can use the Poisson distribution to estimate the expected number of observations in each class. Let z = i = 0.95 be the estimated value of λ. Then the classes can be set up as follows:

Class 0: X = 0

Class 1: X = 1

Class 2: X = 2

Class 3 or more: X ≥ 3

Using the Poisson distribution, we can calculate the expected number of observations in each class:

Class 0: P(X=0; λ=z) × n = e^(-z) × z^0 / 0! × 200 = 18.2

Class 1: P(X=1; λ=z) × n = e^(-z) × z^1 / 1! × 200 = 86.5

Class 2: P(X=2; λ=z) × n = e^(-z) × z^2 / 2! × 200 = 163.8

Class 3 or more: P(X≥3; λ=z) × n = 1 - P(X=0; λ=z) - P(X=1; λ=z) - P(X=2; λ=z) = 31.5

(c) To test the hypothesis that X has a Poisson distribution with parameter λ = 0.95, we can use the chi-squared goodness-of-fit test. The test statistic is given by:

χ^2 = Σ (Oi - Ei)^2 / Ei

where Oi is the observed frequency in the i-th class and Ei is the expected frequency in the i-th class. Using the classes from (b), we can calculate the test statistic:

χ^2 = [(110-18.2)^2 / 18.2] + [(61-86.5)^2 / 86.5] + [(17-163.8)^2 / 163.8] + [(9-31.5)^2 / 31.5] = 137.52

The critical value of chi-squared for 3 degrees of freedom and a significance level of 0.01 is 11.345. Since the calculated test statistic (137.52) is greater than the critical value (11.345), we reject the null hypothesis that X has a Poisson distribution with parameter λ = 0.95. Therefore, there is evidence that the distribution of X is not Poisson.

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Related Questions

Farias car is worth 22000. Of the value of the car decreases by 8% what will her car be worth next year?

Answers

Answer:

$17600

Step-by-step explanation:

Sarah and Ethan are plotting points on a
coordinate grid. Sarah plots the point A(-2. – 3)
and Ethan plots the point B(1.2). What is the
distance between the two points?

Answers

Answer:

srry buddy

I didn't get the answer ✌️✌️

4 Eric sketches a rectangle with a perimeter of
90 inches. The length of the rectangle is three
inches longer than the width. Which equation
can be used to determine x, the width of the
rectangle Eric sketched?
F 2x + 2x + 3 = 90
G 2(x + 3) = 90
H x(x + 3) = 90
J 2(x) + 2(x + 3) = 90

Answers

Answer:

2(x) + 2(x + 3) = 90

Step-by-step explanation:

Width: x inch.

Length: (x + 3) inch.

P = 2 [tex]w^{}[/tex] + 2 [tex]l^{}[/tex]

P = 2(x) + 2(x + 3) = 90

Which is the median of this set of data?
18
22 11 21 78 11
A 20.5
B 21
C 18
D) 19.5

Answers

19.5 is the median. u put all the number in order from least to greatest and find which number is in the middle. since two are in the middle u add the two number together then divide by 2 to find the center of those two numbers. so the answer is therefore D

(1) One apple weighs 75 grams and one orange weighs 40 grams. The weight of x apples and y oranges, is​

Answers

Answer:

Given,

Weight of each apple =75 gm

Weight of each orange =40 gm

So,

Weight of x apples =75x gm

Weight of y oranges =40y gm

Thus,

Weight of x apples and y oranges =(75x+40y) gm

I hope it's helpful!

1. 50% of 82
2. 10% of 2,350
3. 80% of 40
4. 160% of 30
5. 250% of 2
6. 105% of 260
7. 0.5% of 12
8. 40% of 16.5
9. 75% of 8.4
Help please !!

Answers

Answer:

1. 41

2. 235

3. 32

4. 48

5. 5

6. 273

7. .06

8. 6.6

9. 6.3

Step-by-step explanation:

Answer:

1=41

2=235

3=32

4=48

5=5

6=273

7=0.06

8=6.6

9=6.3

Marion is driving between two towns that are close together. If she drives 1/5 the distance of the trip in 15 minutes, what is her rate per hour?

Answers

Answer: 75 minutes per hour.

Step-by-step explanation:

From the question, we are informed that Marion is driving between two towns that are close together and that she drives 1/5 the distance of the trip in 15 minutes.

The rate per hour will then be:

= 15 ÷ 1/5

= 15 × 5

= 75 minutes

The rate per hour will then be 75 minutes per hour.

What graph represents the equationy = 2x – 3?

Answers

Answer:

linear graph

Step-by-step explanation:

because the equation of the line is straight

The cubed root for 50

Answers

Answer:

125000

Step-by-step explanation:

Answer:

125000 is your answer

Step-by-step explanation:

pick me brainliest alex

whats her errors and whats the soulution​

Answers

Answer:

she messed up at -17=34x

Step-by-step explanation:

she added 8x to each side but she was actually supposed to subtract

The error is 8(x - 3) + 7 = 2x(13) and -17 = 34x.

4 - 17 = -13, not 13

8x - 17 = 26x

-17 = 26x -8

-17 = 18x ( it should be like this, but this is still wrong because it should -26)

The solution is:

8(x - 3) + 7 = 2x(4 - 17)

8(x - 3) + 7 = 2x(-13)

8x - 24 + 7 = -26x

8x - 17 = -26x

8x + 26x = 17

34x = 17

x = 17/34

x = 1/2

Hope it helps!

The question is up there ☝

Answers

Answer:

D

Step-by-step explanation:

The parabola is translated down 2 units.

I might be wrong tho.

You deposit $100 in a savings account. The account earns 11% simple interest per year.
a. What is the interest earned after 10 years?
The interest earned is $
after 10 years.
b. What is the balance after 10 years?
The balance is $
after 10 years.

Answers

Answer:

a. ----> $10b. ----> $110

Step-by-step explanation:

principle ( p ) = $100time ( t ) = 10 years rate ( r ) = 11%simple interest = (p × r × t)÷ 100 = ( $100 × 11 × 10 )÷ 100 = 11000 ÷ 100 = $110

interest = simple interest - principle interest = $110 - $100 = $10

MARK ME AS BRAINLIST

PLZ FOLLOW ME

Plsss help me ASAP plss

Answers

The answer is: 9 lte u

I NEED HELP ASAP PLEASE HELP DONT JUST SPAM :(

Answers

Answer:

i think for 4 is b altho im not sure

Step-by-step explanation:

At the end of the summer, I decide to drain the swimming pool
(which has 1500 gallons of water in it). I noticed that it drains
faster when there is more water in the pool. That was interesting
to me, so I decided to measure the rate at which it drains. I found
that it was draining at a rate of 1% every minute.
How long will it take to empty the pool?

Answers

20% is the answer. 20%

Write 9 x 1 + 3 x 1/10 + 4 x 1/ 1000

Answers

Answer:

A

Step-by-step explanation:

A coin is flipped 10 times and lands on heads 8 times. What is the theoretical probability that the coin will land on tails on the next flip?

20%
80%
50%
100%

Answers

Answer:

pls mark brainlest Even though it landed on heads 8/10 times, ther's still a 50% chance that it will land on tails.

NO ONE IS HELPINNGGGG PLZZZZ 30 PTS +brainliest

Answers

Answer:

studyyy that is allll

Step-by-step explanation:

study

Answer:

360°

Step-by-step explanation:

It kind of seems like a trick question, but as far as I'm concerned, it's more or less the same question as the 1st one you answered.

Solve for x
x^2-2x-2=0

Answers

I believe it’s x=1+√3,1−√3

308 miles in 7 hours. Find the
rate and unit rate in miles per
hour. Please help :) It’s 15 points.

Answers

Answer:

They did 44 miles per hour

Step-by-step explanation:

308 / 7 = 44

What are the answers for these,

Answers

3.5 m = 350 cm

9.072 km = 9072 m

0.07 kg = 70 g

70.4 l = 70400 ml

79 m = 0.079 km

6 g = 6000 kg

5,870 m = 5.78 km

61,900 g = 61.9 kg

hallar el color de x en la siguiente figura​

Answers

Step-by-step explanation:

[tex]105 (2 \times - (11)[/tex]

If x is the least common multiple of the set {6, 8, 12} and y is the greatest common factor
of the set {20, 42, 72), what is the value of x/y ?

Answers

Answer:

12

Step-by-step explanation:

The least common multiple of {6,8,12} is 24. This can be intuitively figured by noting that any multiple of 12 is a multiple of 6 and that 12 is 1.5x larger than 8. That means we only have so multiple 12 by 2 and 8 by 3 for them to be equal. The GCF of {20,42,72} is 2 as the prime factorization of 20 is 2x2x5 and 42 is 2x3x7. That means even without having to check 72 (which is clearly even so 2 is a factor), we know that 2 is the greatest common factor that they could share. So X/Y = 24/2 = 12

PLZ HELP WILL MARK BRAINIEST

Today, everything at a store is on sale. The store offers a 20% discount.

The regular price of a T-shirt is $16.

If the regular price of an item is x dollars, what is the discount price in dollars?

a.) 0.2x
b.) 0.8x
c.) 1.2x
d.) none of the above

Answers

Answer:

D?

Step-by-step explanation:

Which angles in the picture are NOT supplementary?
2 and 3; 1 and 4
1 and 2; 2 and 3
1 and 3; 2 and 4
4 and 1; 3 and 4

Answers

Answer:

1 and 3; 2 and 4

Step-by-step explanation:

Supplementary angles add up to 180 degrees, which is a straight line.

we can see that angles 2 and 3 make the / line, as do 1 and 4

1 and 2 make up the \ line, while, as mentioned above, 2 and 3 make /

4 and 1 is the same as 1 and 4 so they still create / and angles 3 and 4 make the \

in a yaz game, Gina won 3 games, lost 5, later won 6 and finally lost 4, what was the balance of the game?​

Answers

Answer:

0

Step-by-step explanation: 3-5=-2+6=4-4=0

The quadrilaterals JKLM and PQRS are similar.
Find the length x of PQ.
P
3
27
M
s
6
x
3.6
K
5
R
45

Answers

Answer:

I believe the answer is 45.

Step-by-step explanation:

This is just my opinion. However I could be wrong.

Answer:

5.4

Step-by-step explanation:

Scale factor = 2.7/3 = 0.9

x = 6*0.9 = 5.4

You deposit $250 in an account. The account earns $20 simple interest in 4 years. What is the annual interest rate?

Answers

Answer:

5.00

Step-by-step explanation:

20/4 years = 5 per year

PLS HELP!!

Solve for a side in right triangles

BC = ???

round your answer to the nearest hundredth

Answers

Answer:

39 centimeters

Step-by-step explanation:

I am very sorry if I'm wrong! ✿✿✿

Prolly wrong but I tried

HELP ME PLEAAAAAAAAAASSSSSSSSE

Answers

Answer:

jwjsjsjwujksikwpqñk1972

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