1, The following table contains the number of successes and failures for three categories of a variable. Test whether the proportions are equal for each category at the α=0.01 level of significance.

_ Category_1   Category_2   Category_3
Failures 69 31 33
Successes 81 32 77

What is the​ P-value?

​(Round to three decimal places as​ needed.)

What conclusion can be​ made?

A.The​ P-value is greater than or equal to α​, so reject H0. There is sufficient evidence that the categories of the variable and success and failure are dependent.

B.The​ P-value is less than α​, so reject H0. There is not sufficient evidence that the categories of the variable and success and failure are dependent.

C.The​ P-value is less than α​, so not reject H0. There is sufficient evidence that the proportions are different from each other.Your answer is not correct.

D.The​ P-value is greater than or equal than α​, so do not reject H0. There is not sufficient evidence that the proportions are different from each other.

Calculate the test statistic.

whats the ​P-value

Suppose that in a simple random sample of 100 people, 69 of them believe the Seahawks will win the Superbowl this year. We want to determine if the proportion of people in the population who believes this is less than 0.75.

Choose the appropriate concluding statement.

a. The sample data do not provide evidence that the proportion of people who believe the Seahawks will win the SuperBowl is less than 0.75.

b. The sample data provide evidence that the proportion of people who believe the Seahawks will win the SuperBowl is less than 0.75.

c. The sample data do not provide evidence that the proportion of people who believe the Seahawks will win the SuperBowl is less than 0.69.

d. The sample data provide evidence that the proportion of people who believe the Seahawks will win the SuperBowl is less than 0.69.

e. The sample data do not provide evidence that the proportion of people who believe the Seahawks will win the SuperBowl is greater than or equal to 0.75.

f. The sample data provide evidence that the proportion of people who believe the Seahawks will win the SuperBowl is greater than or equal to 0.75.

Resuelva cada uno de los ejercicios de pruebas NO paramétricas:

Se han seleccionado aleatoriamente una muestra de 82 estudiantes de Instituto y otra con 46

estudiantes de centros privados y se ha considerado la nota en Educación Física para cada uno

de ellos. Los datos obtenidos vienen resumidos en la siguiente tabla de contingencia.

Institute

1. Se desea contrastar la hipótesis de que la distribución de notas en Educación física es independiente del

             tipo de centro de Enseñanza

English 

sample of 82 Institute students was randomly selected and another with 46

students from private schools and the note in Physical Education has been considered for each

from them. The data obtained are summarized in the following contingency table.

Use the above table

We wish to contrast the hypothesis that the distribution of grades in Physical Education is independent of the type of teaching center

Resuelva cada uno de los ejercicios de pruebas NO paramétricas:

1. La efectividad de la publicidad para dos productos rivales (Marcas X e Y) fueron comparadas. Se hizo una investigación de mercado en un centro comercial local, donde a los participantes se les muestra un aviso publicitario de entre dos productos rivales de marcas de café, los cuales ellos evaluarán en una escala del 1 (definitivamente NO compraré el producto) al 10 (definitivamente SI compraré el producto). A la mitad de los participantes se les mostró el aviso publicitario de un producto mientras que a la otra mitad el del otro producto. Los datos obtenidos son los siguientes:

Aplique una prueba de hipótesis para determinar si ambas marcas tienen la misma aceptación. En caso de no ser así indique que marca es más aceptada. Arroje conclusiones. Calcule el estadístico de prueba. Grafique (Graph) la región de rechazo. Calcule el valor p de la prueba (p-value).

English

Solve each of the non-parametric test exercises:

1. The effectiveness of advertising for two rival products (Trademarks X and Y) were compared. A market research was conducted at a local shopping center, where participants are shown an advertisement from two rival coffee brand products, which they will evaluate on a scale of 1 (I will definitely NOT buy the product) at 10 (I will definitely buy the product). Half of the participants were shown the advertising of one product while the other half of the other product. The data obtained are the following:

use data above

Apply a hypothesis test to determine if both brands have the same acceptance. If not, indicate which brand is more accepted. Throw conclusions. Calculate the test statistic. Graph (Graph) the rejection region. Calculate the p-value of the test (p-value).

A local brewery sells their beer in 330 ml bottles. On average the beer is filled with 328.1 ml with a standard deviation of 0.9 ml. Since it is possible to under-fill the bottle but impossible to fill the bottle with more than 330 ml, the distribution is skewed left. Use this information and Excel functions to answer the following questions, and round your answers to four decimal places.

a. What is the probability that the average fill of a six-pack will be greater than 328.5 ml?   

b. What is the probability that the average fill of a twelve-pack will be greater than 328.5 ml?   

c. What is the probability that the average fill of a twelve-pack will be less than 327.8 ml

Resuelva cada uno de los ejercicios de pruebas NO paramétricas:

Una agencia publicitaria está investigando a qué tipo de avisos le prestan más atención los

adolescentes. Se observan a 11 niños, a 6 se les muestra avisos sobre comida y a los 5 restantes

se les muestra avisos sobre bebidas. Todos los avisos tienen duración similar. Se registra el

tiempo de atención (en segundos) de los 11 niños.

Los datos se resumen a continuación:

Notice type

Ordered Data

1. Aplique una prueba NO paramétrica para determinar si existen diferencias estadísticamente significativas entre ambos grupos. De haberlas, diga cual es el grupo de avisos al que los niños le prestan mayor atención. Muestre todo el procedimiento. Calcule el estadístico, y arroje conclusiones.

English

An advertising agency is investigating what kind of ads pay more attention to
teenagers. 11 children are observed, 6 are shown notices about food and the remaining 5
They are shown warnings about drinks. All notices have a similar duration. The registration is recorded attention time (in seconds) of the 11 children.

The data is summarized above:

Apply a non-parametric test to determine if there are statistically significant differences between both groups. If there are, tell which is the group of notices to which the children pay more attention. Show the whole procedure. Calculate the statistic, and draw conclusions.

Calculate the five-number summary of the given data. 11 7 2 17 18 2 13 22 16 1 20 21 20 23 24

Specify sample spaces for the random experiments (a)-(e) and give mathematical descriptions of the corresponding events. (a) Experiment: A coin is tossed three times. Event: The result of the second toss is “heads”. (b) Experiment: Three indistinguishable coins are tossed at the same time. Event: At most two of the coins show “heads”. (c) Experiment: A die is rolled until each number has appeared at least once. The outcome is the number of rolls needed. Event: Less than 15 rolls are needed. (d) Experiment: n devices labeled with 1, . . . , n are inspected. It is of interest which devices are working and which are not. Event: The first three devices are defective. (e) Experiment: n devices are inspected. Interest lies in the number of defective devices. Event: Exactly three devices are defective.

Difference between Means, Sample size selection.

Explain Confidence Interval for a Mean, Total, Proportion, Standard Deviation.

Methods of Selecting Random Samples.

In a random sample of

8

​people, the mean commute time to work was

35.5

minutes and the standard deviation was

7.3

minutes. A

98%

confidence interval using the​ t-distribution was calculated to be

left parenthesis 27.8 comma 43.2 right parenthesis(27.8,43.2).

After researching commute times to​ work, it was found that the population standard deviation is

8.7

minutes. Find the margin of error and construct a

98%

confidence interval using the standard normal distribution with the appropriate calculations for a standard deviation that is known. Compare the results.

Suppose we have a binomial experiment in which success is defined to be a particular quality or attribute that interests us.

(a) Suppose n = 43 and p = 0.36.

(For each answer, enter a number. Use 2 decimal places.)
n·p =
n·q =

Can we approximate p̂ by a normal distribution? Why? (Fill in the blank. There are four answer blanks. A blank is represented by _____.)

_____, p̂ _____ be approximated by a normal random variable because _____ _____.

first blank

Yes or No    

second blank

can or cannot    

third blank

n·p exceeds

n·p and n·q do not exceed    

n·q exceeds

n·p does not exceed

n·q does not exceed

both n·p and n·q exceed

fourth blank (Enter an exact number.)
__________

What are the values of μ_p̂ and σ_p̂? (For each answer, enter a number. Use 3 decimal places.)
μ_p̂ =

σ_p̂ =

(b) Suppose n = 25 and p = 0.15.

Can we safely approximate p̂ by a normal distribution? Why or why not? (Fill in the blank. There are four answer blanks. A blank is represented by _____.)

_____, p̂ _____ be approximated by a normal random variable because _____ _____.

first blank

Yes or No    

second blank

can or cannot    

third blank

n·p exceeds

n·p and n·q do not exceed    

n·q exceeds

n·p does not exceed

n·q does not exceed

both n·p and n·q exceed

fourth blank (Enter an exact number.)
_____

(c) Suppose n = 56 and p = 0.19.

(For each answer, enter a number. Use 2 decimal places.)
n·p =
n·q =

Can we approximate p̂ by a normal distribution? Why? (Fill in the blank. There are four answer blanks. A blank is represented by _____.)

_____, p̂ _____ be approximated by a normal random variable because _____ _____.

first blank

Yes or No    

second blank

can or cannot    

third blank

n·p exceeds

n·p and n·q do not exceed   

n·q exceeds

n·p does not exceed

n·q does not exceed

both n·p and n·q exceed

fourth blank (Enter an exact number.)

_____
What are the values of μ_p̂ and σ_p̂? (For each answer, enter a number. Use 3 decimal places.)
μ_p̂ =

σ_p̂ =

The speeds of car traveling on Interstate Highway I-35 are normally distributed with a mean of 74
miles per hour and a standard deviation of 6 miles per hour.
(a) Find the percentage of the cars traveling on this highway with a speed
i. of more than 85,
ii. between 65 to 72.
(b) If a BMW is at the speed that is faster than 90 percentage of cars, what is the speed of the
BMW?

Do bonds reduce the overall risk of an investment portfolio? Let x be a random variable representing annual percent return for Vanguard Total Stock Index (all stocks). Let y be a random variable representing annual return for Vanguard Balanced Index (60% stock and 40% bond). For the past several years, we have the following data.

(a) Compute Σx, Σx², Σy, Σy².

(b) Use the results of part (a) to compute the sample mean, variance, and standard deviation for x and for y. (Round your answers to two decimal places.)

(c) Compute a 75% Chebyshev interval around the mean for x values and also for y values. (Round your answers to two decimal places.)

Use the intervals to compare the two funds.

a. 75% of the returns for the balanced fund fall within a narrower range than those of the stock fund.

b. 75% of the returns for the stock fund fall within a narrower range than those of the balanced fund.    

c. 25% of the returns for the balanced fund fall within a narrower range than those of the stock fund.

d. 25% of the returns for the stock fund fall within a wider range than those of the balanced fund.

(d) Compute the coefficient of variation for each fund. (Round your answers to the nearest whole number.)

Use the coefficients of variation to compare the two funds.

a. For each unit of return, the stock fund has lower risk.

b. For each unit of return, the balanced fund has lower risk.    

c. For each unit of return, the funds have equal risk.

If s represents risks and x represents expected return, then s/x can be thought of as a measure of risk per unit of expected return. In this case, why is a smaller CV better? Explain.

a. A smaller CV is better because it indicates a higher risk per unit of expected return.

b. A smaller CV is better because it indicates a lower risk per unit of expected return.

4. You have collected weekly earnings and age data from a sub-sample of 1,744 individuals using the Current Population Survey in a given year.

(a) Given the overall mean of $434.49 and a standard deviation of $294.67, construct a 99% confidence interval for average earnings in the entire population. State the meaning of this interval in words, rather than just in numbers. If you constructed a 90% confidence interval instead, would it be smaller or larger? What is the intuition?

(b) When dividing your sample into people 45 years and older, and younger than 45, the information shown in the table is found.

Test whether or not the difference in average earnings is statistically significant. Given your knowledge of age-earning profiles, does this result make sense?

Let X~BIN(40,0.1). Let Y=max(0,x-3). FindE[Y].