(Round the final answer to 4 decimal digits) 1. A brand name has a 70% recognition rate. Assume the owner f the brand wants to verify that rate by begging with a small sample of 6 randomly select consumers. a. What is the probability that exactly 4 of the selected consumers recognize the brand name?

b. What is the probability that all of the selected consumers recognize the brand name?

c. What is the probability that at least 5 of the selected consumers recognize the brand name?

d. What is the probability that at most 2 of the selected consumers recognize the brand name?

2) . The lengths of pregnancies are normally distributed with a mean of 272 days and a standard deviation of 15 days. If 35 women are randomly selected, find the probability that they have a mean pregnancy between 271 days and 275 days.

3) The body temperatures of adults are normally distributed with a mean of 98.6° F and a standard deviation of 0.50° F. If 25 adults are randomly selected, find the probability that their mean body temperature is greater than 98.4° F.

4) The average number of pounds of red meat a person consumes each year is 190 with a standard deviation of 24 pounds (Source: American Dietetic Association). If a sample of 60 individuals is randomly selected, find the probability that the mean of the sample will be Less than 192 pounds.

19. Classify the following statement as an example of classical​ probability, empirical​ probability, or subjective probability. Explain your reasoning.

The probability that a randomly selected number from 1 to 400 is divisible by 6 is 0.165.

This is an example of ___ probability since ____.

18.Classify the following statement as an example of classical​ probability, empirical​ probability, or subjective probability. Explain your reasoning.

According to a​ survey, the probability that an adult chosen at random is in favor of a tax cut is about 0.49

This is an example of ___ ​probability, since ___.

17.Classify the following statement as an example of classical​ probability, empirical​ probability, or subjective probability. Explain your reasoning.

An analyst feels that a certain​ stock's probability of increasing in price over the next week is 0.66

This is an example of ___ ​probability, since___

16.Classify the following statement as an example of classical​ probability, empirical​ probability, or subjective probability. Explain your reasoning.

The probability of choosing 6 numbers from 1 to 58 that match the 6 numbers drawn by a certain lottery is 1/40,475358 ≈0.00000002

This is an example of ___ ​probability, since ___

15.Classify the following statement as an example of classical​ probability, empirical​ probability, or subjective probability. Explain your reasoning.

According to company​ records, the probability that a washing machine will need repairs during a ten​-year period is 0.09.

This is an example of ___ ​probability, since____

A sports psychologist is part of a team of researchers collecting descriptive psychological, mental, performance and physiological data on male and female high school athletes. One of the variables is Intelligence Quotient (IQ) as assessed by the Stanford-Binet Intelligence Scale (5^th Ed. 2003). A sample of athletes (n=61) provided the following statistics: mean±s_X = 97±16. The parameter µ for IQ is thought to be 100.   Test H₀: X=µ at α=0.05÷2 (a 2-tailed test).

The better-selling candies are often high in calories. Assume that the following data show the calorie content from samples of M&M's, Kit Kat, and Milky Way II.

Assuming we don't know about the shape of the population distribution, use the Kruskal-Wallis Test to test for significant differences among the calorie content of these three candies.

State the null and alternative hypotheses.

H₀: Not all populations of calories are identical.
H_a: All populations of calories are identical.H₀: All populations of calories are identical.
H_a: Not all populations of calories are identical.    H₀: Median_MM = Median_KK = Median_MW
H_a: Median_MM > Median_KK > Median_MWH₀: Median_MM ≠ Median_KK ≠ Median_MW
H_a: Median_MM = Median_KK = Median_MWH₀: Median_MM = Median_KK = Median_MW
H_a: Median_MM ≠ Median_KK ≠ Median_MW

Find the value of the test statistic. (Round your answer to two decimal places.)

Find the p-value. (Round your answer to three decimal places.)

p-value =

At a 0.05 level of significance, what is your conclusion?

Do not reject H₀. There is sufficient evidence to conclude that there is a significant difference among the calorie content of these three candies.Reject H₀. There is not sufficient evidence to conclude that there is a significant difference among the calorie content of these three candies.    Do not reject H₀. There is not sufficient evidence to conclude that there is a significant difference among the calorie content of these three candies.Reject H₀. There is sufficient evidence to conclude that there is a significant difference among the calorie content of these three candies.

A random sample size of 1000 school children from urban areas shows average height is 150cm with an S.D. of 45.2cm. Similar sample of students from rural school has average height of 146 cm. with an SD of 37.3cm. Are students from urban area taller than students from rural area?

Use data below to complete

Table 1.18 Frequency of Number of Movies Viewed

Table 1.19 Frequency of Number of Movies Viewed

1. Using the tables, find the percent of data that is at most two. Which table did you use and why?
2. Using the tables, find the percent of data that is at most three. Which table did you use and why?
3. Using the tables, find the percent of data that is more than two. Which table did you use and why?
4. Using the tables, find the percent of data that is more than three. Which table did you use and why?

Discussion Questions

1. Is one of the tables “more correct” than the other? Why or why not?
2. In general, how could you group the data differently? Are there any advantages to either way of grouping the data?
3. Why did you switch between tables, if you did, when answering the question above?

Where would I find five sets of data that produces a correlation of .56 between the variables?

Design a correlational study that will need two variables with at least five sets of data. between these two variables: time spent playing video games and aggression.

Then in 500-750 words, do the following:

Assume the study produces a correlation of .56 between the variables. Analyze three possible causal reasons for the relationship.

Submit an SPSS output for the correlational study.

Assume that X and Y has a continuous joint p.d.f. as (28x^2)*(y^3) in 0<y<x<1 interval. Otherwise the joint p.d.f. is equal to 0.

1. Prove that the mentioned f(x,y) is a joint probability density function.
2. Calculate E(X)
3. Calculate E(Y)
4. Calculate E(X2)
5. Calculate Var(X)
6. Calculate E(XY)
7. Calculate P(X< 0.1)
8. Calculate P(X> 0.1)
9. Calculate P(X>2)
10. Calculate P(-2<X<0.1)

In a study of monthly salary distribution of residents in Paris conducted in year 2015, it was found that the salaries had an average of €2200 (EURO) and a standard deviation of €550. Assume that the salaries were normally distributed.

In 2017, a study on the salary distribution of Paris residents was conducted. Assume that the salaries were normally distributed. A random sample of 10 salaries was selected and the data are listed below:

Question 1: Assume that the standard deviation of the salaries was still the same as in 2015. Estimate the average salary (in 2017) with 95% confidence.

Question 2: The assumption made in Question 8 was certainly unrealistic. Estimate the average salary (in 2017) with 95% confidence again assuming that the standard deviation had changed from 2015.

Question 3: Estimate the variance of monthly salaries of Paris residents (in 2017) based on the sample provided above at a 95% confidence level.

A similar study was conducted on salary distribution of Paris residents in 2019. The research team aimed to estimate the average salary. They chose the 98% confidence and assumed that the population standard deviation was the same as in 2015. Assume again that those salaries were normally distributed.

Question 4 :If they would like the (margin of) error to be no more than €60, how large a sample would they need to select? (That is, find the minimum sample size.)

Select one:

A: 322

B: 323

C: 456

D: 457

2. [Uncertainty and risk] A DM is presented with two jars. Jar 1 has 50 red and 50 blue balls. Jar 2 consists of 100 total balls each of which is either red or blue but the colors are in an unknown proportion. An experiment consists of drawing a single ball from each jar. The DM faces the following two choices. Choice 1 is between option 1a which pays $100 if the Jar 1 ball is red, and option 1b which pays $100 if the Jar 2 ball is red (and $0 otherwise). Choice 2 is between option 2a which pays $100 if the Jar 1 ball is blue, and option 2b which pays $100 if the Jar 2 ball is blue (and $0 otherwise). Suppose the DM chooses 1a over 1b and 2a over 2b (and has a strict preference in each case).

Are these choices consistent with subjective EU? In other words, does there exist a probability distribution over the contents of Jar 2 (that is, a belief that the proportion of Red balls is p and of Blue balls is 1-p) such that, given these beliefs, the choices of the DM can be rationalized by expected utility? If so, provide the subjective probabilities that rationalize the choices. If not, argue that there are no such probabilities. [Note: Because the outcomes are only $0 and $100, risk preferences play no role here. That is, all utility functions for which u($100) > u($0) are observationally equivalent on these choices. Notice that in order for the curvature of the utility function to be relevant, one would need to consider at least three wealth levels. This is the reason that I am asking only about probabilities and not also about the utility function in this question.]

Last rating period, the percentages of viewers watching several channels between 11 p.m. and 11:30 p.m. in a major TV market were as follows:

Suppose that in the current rating period, a survey of 2,000 viewers gives the following frequencies:

(a) Show that it is appropriate to carry out a chi-square test using these data.

Each expected value is ≥         

(b) Test to determine whether the viewing shares in the current rating period differ from those in the last rating period at the .10 level of significance. (Round your answer to 3 decimal places.)

χ2χ2          

(Click to select)Do not rejectReject H₀. Conclude viewing shares of the current rating period (Click to select)differdo not differ from those of the last.

The PACE project at the University of Wisconsin in Madison deals with problems associated with high-risk drinking on college campuses. Based on random samples, the study states that the percentage of UW students who reported bingeing at least three times within the past two weeks was 42.2% in 1999 (n = 334) and 21.2% in 2009 (n = 843). Test that the proportion of students reporting bingeing in 1999 is different from the proportion of students reporting bingeing in 2009 at the 10% significance level.

(A.1) Construct a 90% confidence interval around the difference-in-proportions estimate. Enter the lower bound of the interval you calculated in the box below. (In this case, be sure to use the standard error you calculated when determining the test statistic that uses information about the population proportion.)

(A.2) Construct a 90% confidence interval around the difference-in-proportions estimate. Enter the upper bound of the interval you calculated in the box below. (In this case, be sure to use the standard error you calculated when determining the test statistic that uses information about the population proportion.)

(B.1) How would you interpret the confidence interval?

(B.2) What connections can you draw between the confidence interval and the hypothesis test?(Because zero falls outside/inside the confidence interval, we reject/fail to reject the null hypothesis.)

• What is a factorial ANOVA?
• How does this compare to an ANOVA?
• What is the research design for factorial ANOVAs and MANOVAs?

Consider the following gasoline sales time series. If needed, round your answers to two-decimal digits.