A coin is thrown until a head occurs and the number X of tosses recorded. After repeating the experiment 256 times, we obtained the following results:x 1 2 3 4 5 6 7 8f 136 60 34 12 9 1 3 1Test the hypothesis, at the 0.05 level of significance, that the observed distribution of X may be fitted by the geometric distribution g(x ; 1 / 2), x=1,2,3

Answers

Answer 1

The hypothesis, at the 0.05 significance level,

H₀ : the observed distribution of X may be fitted by the geometric distribution

Hₐ : the observed distribution of X may not be fitted by the geometric distribution

we conclude p-Value > α so, cannot reject null hypothesis. The observed distribution of X may be fitted by the geometric distribution g(x ; 1 / 2), x=1,2,3

A coin is thrown until a head occurs and the number X of tosses recorded.

The probability that head occur on toss ,p = 0.5

Consider the null and alternative hypothesis,

H₀ : the observed distribution of X may be fitted by the geometric distribution

Hₐ : the observed distribution of X may not be fitted by the geometric distribution

The chi square test statistic here as:

χ² = ∑( Oᵢ - Eᵢ)²/Eᵢ

where Oᵢ--> observed value

Eᵢ --> expected value

and the expected frequencies for each X here E(x) = P(X = x) = 256×g(x)

The probability mass function of geometric distribution with parameter 1/2 is g(x) = (1/2)(1 - 1/2)⁽ˣ⁻¹⁾

where x = 0, 1,2 ,3,......

Observed values are f :136 60 34 12 9 1 3 1

Using the data,we calculate the expected values

E₁ = P( x = 1) = 256×g(1) = 256×(1/2)(1/2)⁰

= 128

E₂ = P( x =2) = 256×g(2) = 256×(1/2)(1/2)¹

= 64

E₃ = P( x = 3) = 256×g(3) = 256×(1/2)(1/2)² = 32

E₄ = P( x = 4) = 256×g(4) = 256×(1/2)(1/2)³

= 16

E₅ = P( x = 5) = 256×g(5) = 256×(1/2)(1/2)⁴

= 8

E₆ = P( x = 6) = 256×g(6) = 256×(1/2)(1/2)⁵

= 4

E₇ = P( x = 7) = 256×g(7) = 256×(1/2)(1/2)⁶

= 2

E₈ = P( x = 8) = 256×g(8) = 256×(1/2)(1/2)⁷

= 1

Hence, χ² = ∑( Oᵢ - Eᵢ)²/Eᵢ

= (136 - 128)²/128 + (60 - 64)²/64 + (34 - 32)²/32 + (12-16)²/16 +(9 - 8)²/8 + (1 - 4 )²/4 + (3 - 2)²/2 +(1 - 1)²/1

= 0.5 + 0.25 + 0.125 + 1 + 0.125 + 2.25 + 0.5 =4.75

Significance level is α =0.05

Using the χ² table, the p- value for χ² is 0.6290 .. Now P value > 0.05 , therefore the test is not significant here and we cannot reject the null hypothesis here. Therefore we have sufficient evidence here that the frequencies given are fitted by the geometric (p = 0.5) distribution.

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A Coin Is Thrown Until A Head Occurs And The Number X Of Tosses Recorded. After Repeating The Experiment

Related Questions

There are 920 calories in 5 servings. Find the unit rate.

Answers

Answer:

184

Step-by-step explanation:

920 divided by 5 is 184 which makes it unit rate

Heeeeeeeelp pleaaase

Answers

Answer:

13u√2u

Step-by-step explanation:

Remark

Removing factors from under the square root sign means factoring the numbers into prime factors. If there are an even number of equal prime factors, take one out and throw one away for all the primes that are the same. An odd number of factors always leaves 1 under the root sign.

For example

u^3 = u * u * u

One of the u's will be left behind. Of the two others, one will be discarded and one will be taken outside the root sign.

√u^3 = √(u * u * u) = u√u

one u taken out. 1  u left behind 1  u discarded.

Question Breakdown

8√72u^3 = 8√2*2*2*3*3 u^3 = 8* 2*3 * u * √2u = 48u*√2u7√128u^3 = 7√(2*2*2*2*2*2*2 u^3) = 7*2*2*2 √2u = 56u√2u3u*√98u = 3u * √(7*7 * 2*u) = 21u√2u

Answer

48u√2u - 56√2u + 21u√2u

13u√2u

I need help on the pcture​

Answers

Answer:

Where is it?

Step-by-step explanation:

You need to add a picture

This data shows the number of sit-ups done by 27 students in a gym class.
58 62 49 52 75 86 88 54 56 61 85 48 77 60
47 58 62 73 78 69 65 84 59 67 53 84 50
Which histogram represents the data?

Answers

Answer:

C

Step-by-step explanation:

None of the others have the correct data like C

HURRY! What is the circumference of the circle below? Use 3.14 for π.

Answers

Answer:

2.14 divided by 5 x 2 is the ansewer

Step-by-step explanation:

A bottled water distributor wants to determine whether the mean amount of water contained inâ 1-gallon bottles purchased from a nationally known water bottling company is actually 1 gallon. You know from the water bottling company specifications that the standard deviation of the amount of water is 0.008 gallon. You select a random sample of 50 bottles, and the mean amount of water perâ 1-gallon bottle is 0.995 gallon.

Required:
a. Is there evidence that the mean amount is different from 1.0 gallon?
b. What is the test statistic?
c. Compute theâ p-value and interpret its meaning.
d. Construct a 95% confidence interval estimate of the population mean amount of water perâ 1-gallon bottle.

Answers

Answer:

1. There is evidence that mean is different from 1.0 gallon

2. test statistic = -4.42

3. p value = 0.00001

4. 0.9928,0.9972

Step-by-step explanation:

h0: u = 1.0

h1: u not equal to 1.0

alpha = 0.05

sd = 0.008

n = 50

mean = 0.995

standard error se = 0.008/√50 = 0.00113

test statistics calculation

0.995-1/0.00113

= -0.005/0.00113

= -4.42

p value calculation

using the z test statistics and alpha = 0.05

the p value using a p value calculator = 0.00001

0.00001<0.05

so we Reject the null hypothesis

we conclude there is enough evidence that mean is different from 1.0

95% confidence interval

Z alpha/2 = 0.025

we find z value using excel function

NORMSINV (0.025)

|Z| = 1.96

Standard error se = 0.00113

margin of error E = 1.96 x 0.00113 = 0.0022148

confidence interval =

0.995 - 0.0022148, 0.995 + 0.0022148

= 0.9928, 0.9972

find the vertex h(r)=r^(2)+11r-26 PLEASE HELP ME FIGURE THIS OUT

Answers

Answer: Look at the picture

Step-by-step explanation: Hope this help :D

A random sample of 146 recent donations at a certain blood bank reveals that 81 were type A blood. Does this suggest that the actual percentage of type A donations differs from 40%, the percentage of the population having type A blood

Answers

Answer:

We reject H₀  the actual percentage of type A donations differs from 40%

Step-by-step explanation:

Sample information:

sample size   n = 146

Type A   x₁  =  81   and   p₁  = 81 / 146     p₁  =  0,5547

then  q₁   =  1 - p₁    q₁  =  1  -  0,5547    q₁  =  0,4453

We choose as significance level  α  = 5%  α = 0,05   α /2  = 0,025

from z-table we find   z (c) = 1,96

National % of the population  ( μ  = 40 %  μ = 0,4 )

Test hypothesis

Null hypothesis                           H₀           p₁  =  μ

Alternative Hypothesis              Hₐ           p₁   ≠ μ

The Alternative hypothesis indicates that the test is a two-tail test

z(s) =  ( p₁  -   μ )/ √ p₁*q₁ / n

z(s) =  ( 0,5547  -  0,40 )/ √ 0,5547*0,4453 / 146

z(s) =  0,1547 / 0,041

z(s) = 3,77

Comparing  z(s)  and z(c)

z(s) > z(c)  

z(s) is in the rejection region. We reject H₀. Sample does not give evidence to support that the actual percentage of type A donations is equal to the national population

I need help will mark brainlist

When solving -1/8 (x + 35) = - 7, what is the correct sequence of the operations?

1. multiply each side by -1/8, add 35 to each side

2. multiply each side by -1/8, subtract 35 from each side

3. multiply each side by -8, subtract 35 from each side

4. multiply each side by -8, add 35 to each side​

Answers

Answer:

The correct option is 3.

Step-by-step explanation:

By multiplying each side by -8, you can get rid of the fraction. Then by subtracting 35 from both sides, you get what is x.

The Yert family hires a landscaping company for 30 weeks. There are two companies to choose from. Green Lawns charges 1 for the first time they service your lawn, and the price will multiply by a factor of 0.90 every week thereafter. Green Thumbs charges 400 for the first time they service your lawn, and then charges an additional 45 every week thereafter. At 30 weeks, if the Yert family chooses the company that is cheaper, how much money will they save?

Answers

Do you need help or u just wanted the answer

hi can anyone help me with this

Answers

Answer:

i think you should multiply 6cm by 8 cm by 10 cm ..sorry if it was not vlear but i try:)

Solve for x.



O 72.5
O 31.6
O 26
O 11.9

Answers

answer 11.9


D aka))h)

sorry if its twisted but i need help in # 3 please :)

Answers

Answer:

knsy standard ka question hy

Step-by-step explanation:

What is the product of -8 and -7

Answers

Answer:56

Step-by-step explanation: -8x-7=56

Answer: -15

Step-by-step explanation: it will just give you a higher negative number it is literally the opposite from positive equations if u have to negative numbers u add them if there is a negative AND a positive then you substract them :)

In a clothing store, 65% of the customers buy a shirt, 30% of the customers buy a pair of pants, and 20% of the customers buy both a shirt and a pair of pants. I’m f a customer is chosen at random, what is the probability that he or she buys a shirt or a pair of pants?

Answers

Answer:

The Answer will be (0.75)

HELP MEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE

Answers

Answer:

6/13

Step-by-step explanation:

6/13 is the right answer. Goodluck



I need help please fast .................

Answers

Answer:

I have no idea what sohcahtoa is but:

tan 50.1° = x/5

1.196 = x/5

multiply both sides of the equation by 5:

x = 5.98

Find the third quartile Q3 of the list of 24 sorted values shown below.
30 31 31 37 38 38 39 39 42 42 43 46 47 48 50 52 54 57 61 63 68 69 76 79
The third quartile Q3 is
(Type an integer or a decimal.)

Answers

Answer:

60

Step-by-step explanation:

The computation of the third quartile is given below:

The third quartile Q3 is

= 3(n + 1)÷ 4

= 3 (24 + 1) ÷ 4

= 75 ÷ 4

= 18.75th term

Now the 18.75th term is

= 18th term + 0.75 term

= 57 +  (19 term - 18term)

= 57 +  0.75 (61 - 57)

= 57 + 0.75 (4)

= 60

(4-3i)(1+2i)
I have so many of these

Answers

Answer:

-6i^2+5i+4

Step-by-step explanation:

Rearrange Terms

(-3i+4)(1+2i)

(-3i+4)(2i+1)

Distribute

-3(2i+1)+4(2i+1)

-6i^2-3i+4(2i+1)

-6i^2-3i+4(2i+1)

-6i^2-3i+8i+4

Combine Liker Terms

-6i^2+5i+4

Solution

-6i^2+5i+4

Answer:

-2 + 5i

Step-by-step explanation:

Remember these rules:  

real times real = real (e. g., 4(1) = 4)

real times imaginary:  imaginary (e. g., 4(2i) = 8i)

imaginary times real imaginary

imaginary times imaginary:  real with a negative sign (e. g., (-3i)(2i) = +6

          Once again:  work out (-3i)(2i).  We get (i^2)(-6) = +6

In summary:  your (4-3i)(1+2i) becomes 4 + 8i - 3i - (i^2)(-6), or

                                                                 4 + 5i - 6, or   -2 + 5i

Pls help 10 ptsssssssssssss
NO LINKS

Answers

4.5. 4x4.5=18. 18 divided by 4 is 4.5

I pick a ball from a bag, replace it and then pick
another. I keep doing this until I have chosen 40 balls. If I picked out 12 yellow balls, estimate the probability of not picking out a yellow ball.

Answers

Answer:

It should be 50%

Step-by-step explanation:

It should be 50% because there are 12 yellow balls, so it should be 50%.

Hope it helps you

help me please and answer correctly people answer wrong on purpose ​

Answers

Sorry for not answering your question but please I am telling you guys don’t fall for someone when they send you links here like this first person above me he send a link don’t press it y’all don’t this is really bad it makes your phone really bad

For the rectangle shown, which equation can be used to find the value of x?​

Answers

Answer:

Pythagorean theorem [tex]a^{2} +b^{2} =c^{2}[/tex]

Step-by-step explanation:

[tex]a^{2} +b^{2} =c^{2} \\x^{2} +3.6^{2} =7.4^{2} \\x^{2} +12.96=54.76\\x^{2} =\sqrt{41.8} \\x=6.47\\[/tex]

The value of x is 6.46 inch.

What is Pythagoras theorem?

Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“.

Given: breadth = 3.6, diagonal= 7.4

Using Pythagoras theorem,

H²=P²+B²

(7.4)²= (3.6)²+B²

54.76=12.96 + B²

54.76-12.96=B²

41.8= B²

B= 6.46 inch.

Hence, the value of x is 6.46 inch.

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what is the measure of A, in degrees, in the figure shown?

Answers

Answer:

[tex]12.7[/tex]

Step-by-step explanation:

[tex]180 - 167.3 = 12.7 \\ < angle \: on\: a \: stright \: line \: is \: 180[/tex]

The Table shows the relationship and speeds between a cheetah and a line. What is the missing value in the table?

Cheetah (miles per hour)
7 14 ? 28 35

Lion (miles per hour)
5 10 15 20 25

A. 19
B. 21
C. 23
D. 25


Please help ASAP!!

Answers

B because the lions you count by 5 and the cheetahs you count by 7 14+7= 21

x = -3.
3.2 2 - 16=(x-1)=?

Answers

Answer:

dvide it

Step-by-step explanation:

Algebraic Expression:
There are c cyclists in a cycle race. 3/4 of the cyclists finish the race. How many cyclists did not finish the race?

Answers

Answer:
c - 3/4
Explanation:
Subtract 3/4 from c to find how many cyclists did not finish the race.

Determine which point is part of the solution set to the following
system of inequalities: f(x) < x + 4; f(x) > - X-3; and f(x) < 5.
(0,0)
(-60)
(-3, 4)
(4,6)

Answers

I think 4,6
I had a test similar I’m not the best at it though hope this helps tho

In the triangle below,
x = [ ? ] cm. Round to the
nearest tenth.
15 cm
х
350
9.00
y

Answers

Answer:

x=8.6

Step-by-step explanation:

x=8.6

Find the slope of the line (2,6) and (-2,-4)

Answers

10/8
Hope this helped
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