A person drilled a hole in a die and filled it with a lead​ weight, then proceeded to roll it 200 times. Here are the observed frequencies for the outcomes of​ 1, 2,​ 3, 4,​ 5, and​ 6, respectively: 28​, 29​, 40​, 41​, 28​, 34. Use a 0.10 significance level to test the claim that the outcomes are not equally likely. Does it appear that the loaded die behaves differently than a fair​ die

Solution :

The objective of the study is to test the claim that the loaded die behaves at a different way than a fair die.

Null hypothesis, [tex]$H_0:p_1=p_1=p_3=p_4=p_5=p_6=\frac{1}{6}$[/tex]

That is the loaded die behaves as a fair die.

Alternative hypothesis, [tex]$H_a$[/tex] : loaded die behave differently than the fair die.

Number of attempts , n = 200

Expected frequency, [tex]$E_i=np_i$[/tex]

                                        [tex]$=200 \times \frac{1}{6} = 33.333$[/tex]

Test statistics, [tex]$x^2= \sum^6_{i=1} \frac{(O_i-E_i)^2}{E_i} $[/tex]

                            [tex]$=\frac{(28-33.333)^2}{33.333}+\frac{(29-33.333)^2}{33.333}+\frac{(40-33.333)^2}{33.333}+\frac{(41-33.333)^2}{33.333}+\frac{(28-33.333)^2}{33.333}+$[/tex][tex]$\frac{(34-33.333)^2}{33.333}$[/tex]

≈ 5.8

Degrees of freedom, df = n - 1

                                       = 6 - 1

                                       = 5

Level of significance, α = 0.10

At α = 0.10 with df = 5, the critical value from the chi square table

[tex]$x^2_{\alpha}= \text{chi inv}(0.10,5)$[/tex]

     = 9.236

Thus the critical value is [tex]$x_{\alpha}^2=9.236$[/tex]

[tex]$P \text{ value} = P[x^2_{df} \geq x^2]$[/tex]

             [tex]$=P[x^2_5\geq 5.80]$[/tex]

             = chi dist (5.80, 5)

             = 0.3262

Decision : The value of test statistics 5.80 is not greater than the critical value 9.236, thus fail to reject [tex]$H_o$[/tex] at 10% LOS.

Conclusion : There is no enough evidence to support the claim that the loaded die behave in a different than a fair die.

Solve correctly and I’ll give brainliest.

Triangle B is a(n) ______________________ of Triangle A?
A) Reduction
B) Enlargement

I need help with this plz percent equations the question is blank % of 35 = 21

If 12 oranges cost 5.04 how much does 1 orange cost

A recipe says that 2 cups of dry rice will serve 6 people. Complete the table as you answer the questions. Be prepared to explain your reasoning.

In a grocery store, a packet of chips that usually costs $12 is on sale for 30% off. What is the sale price after the discount?

Merida wrote the table of points below. Which explains whether or not Merida has described a proportional relationship, and why?

Solve the following system by using substitution:
x = -3y - 17
2x + 3y = -7

Given the function f(x)= x^4 - 4x^3 -2, determine the absolute minimum value of ff on the closed interval [-2, 4].

2.) Jennifer bought a shirt at Forever 21 for $21.50 after a 3% sales tax. What was the original price of the shirt?

Pls answer and expplain how you got it

How long will it be from December 18 from 8:25 am to December 24 to 4.30 pm

Round 79.045 to the nearest tenth

According to a recent​ survey, the probability that the driver in a fatal vehicle accident is female​ (event F) is 0.2805. The probability that the driver is 24 years old or less​ (event A) is 0.1759. The probability that the driver is female and is 24 years old or less is 0.0424. Answer parts​ (a) through​ (d) below.

(a) Find the probability of FUA. P (FUA)Round to four decimal places as needed.)

(b) Find the probability of F'UA. P(FUA) (Round to four decimal places as needed.)

(c) Find the probability of FnA'

HELPPP ASAP WILL MARK BRAINILEST

A taxi in myrtle beach charges $2 per mile and $1 per person. If a taxi cab ride for 2 people cost $12, how far did the taxi cab travel ( don’t include units (miles) in the answer)

ms. daring just finished a 7 mile run.
how long (in minutes) do you think it took ms. daring (she ran cross country in college even though she is more of a sprinter!)​

Each week, high school students can collect a maximum of 347 cans of food for the town food pantry. What is the maximum number of cans that the high school students can collect in 35 weeks?
10,410 cans
10,415 cans
12,145 cans
12,245 cans

HELPPP FASTTT PLEASE

GEOMETRY-TRIG

Rampy Ronald is fixing to make a jump with his dirt bike across an 80-foot ravine full of lava. The ramp he’s going to hit to make the jump is 15 feet long, forms a 30° with the ground and ends 5 feet from the edge of the ravine. That said, if he hits the ramp at his bike’s full speed of 60mph, he’ll reach a maximum height of 30 feet.

6. From the start of the ramp to when he reaches his maximum height, how far will Rampy Ronald have traveled horizontally?

7. Is Rampy Ronald going to make the jump, or is he fixing to land in the ravine of lava and become Roasty Ronald? Give geometric constructions backed by mathematics to support your reasoning!!!

Find the percent increase. Round to the nearest percent.

From 95 books to 139 books.

The percent increase is __%

(I just need the answer, no need for explanation)

fasfasdasfsadasfsadsfasdsad

Yo can I get some help on this question please

what is an equivalent fraction to 3/8 ​? Find a common denominator for the pair of fractions.​ Then, write equivalent fractions with the common denominator. 3/8 and 9/28

Find the slope of the line that passes through
(10, 1) and (5,2)

3 facts about "What is a Hurricane"?​

Gabrielle is 8 years older than Mikhail. The sum of their ages is 58. What is Mikhail's age?

Your aunt and uncle took turns driving on a 580-mile trip that took 10 hours. Your uncle drove at a constant speed of 60 mph and your aunt drove a constant speed of 55 mph. How long did each person drive?

A. Write the two equations.

B Solve the equations and give both answers.

Derive the equation, in the
form y = mx + b, for the line. (Look at the photo.)

Find the total area:
8 cm
16 cm
29 cm
22 cm

What is the solution for x in the
system of the following
equations?
3x+4 y= 31
3x-4 y=-1