Are there gender differences in the time spent using on social media? A time-tracking software was used to determine the average time on social media websites in a random sample of 31 men and 31 women. Men, on average, spent 49 minutes per day on social media websites, with the standard deviation of 25. Women, on average, spent 52 minutes per day on social media websites, with a standard deviation of 18. Use α=0.05.

Your company has been testing two flavors of coffee using free samples, let's call them Flavor A and Flavor B. You are planning to only offer one flavor for sale and are interested in whether your customers prefer Flavor A or Flavor B.

You use a taste testing survey of 60 randomly selected people, and find that 36 people prefer Flavor B.

Using greta and assuming a generative model with Bernoulli data (X) and a Beta prior (θ):

X∼Bernoulli(θ)

Θ∼Beta(2,2)

determine what your updated probability is that Flavor B is preferred to Flavor A. In other words, what percentage of your posterior draws have a theta that is above 0.5?

(Enter answer as a decimal - i.e. 12% would be entered as 0.120. Round to the nearest thousandths place)

Please show me how something like this would be solved using R.

Explain the difference between a confidence interval and credible interval?

Assume the following for a paired-samples t test: N = 19, M_difference = 13.19, s = 22.3. What is the 95 percent confidence interval for a two-tailed test?

S²(n-1) / σ² is distributed X²(n-1) when ........?

When σ is unknown and the sample is of size n ≥ 30, there are two methods for computing confidence intervals for μ. Method 1: Use the Student's t distribution with d.f. = n − 1. This is the method used in the text. It is widely employed in statistical studies. Also, most statistical software packages use this method. Method 2: When n ≥ 30, use the sample standard deviation s as an estimate for σ, and then use the standard normal distribution. This method is based on the fact that for large samples, s is a fairly good approximation for σ. Also, for large n, the critical values for the Student's t distribution approach those of the standard normal distribution. Consider a random sample of size n = 41, with sample mean x = 44.6 and sample standard deviation s = 5.7. (a) Compute 90%, 95%, and 99% confidence intervals for μ using Method 1 with a Student's t distribution. Round endpoints to two digits after the decimal. 90% 95% 99% lower limit upper limit (b) Compute 90%, 95%, and 99% confidence intervals for μ using Method 2 with the standard normal distribution. Use s as an estimate for σ. Round endpoints to two digits after the decimal. 90% 95% 99% lower limit upper limit (c) Compare intervals for the two methods. Would you say that confidence intervals using a Student's t distribution are more conservative in the sense that they tend to be longer than intervals based on the standard normal distribution? Yes. The respective intervals based on the t distribution are shorter. Yes. The respective intervals based on the t distribution are longer. No. The respective intervals based on the t distribution are shorter. No. The respective intervals based on the t distribution are longer. Correct: Your answer is correct. (d) Now consider a sample size of 71. Compute 90%, 95%, and 99% confidence intervals for μ using Method 1 with a Student's t distribution. Round endpoints to two digits after the decimal. 90% 95% 99% lower limit upper limit (e) Compute 90%, 95%, and 99% confidence intervals for μ using Method 2 with the standard normal distribution. Use s as an estimate for σ. Round endpoints to two digits after the decimal. 90% 95% 99% lower limit Incorrect: Your answer is incorrect. upper limit (f) Compare intervals for the two methods. Would you say that confidence intervals using a Student's t distribution are more conservative in the sense that they tend to be longer than intervals based on the standard normal distribution? Yes. The respective intervals based on the t distribution are shorter. Yes. The respective intervals based on the t distribution are longer. No. The respective intervals based on the t distribution are longer. No. The respective intervals based on the t distribution are shorter. Correct: Your answer is correct. With increased sample size, do the two methods give respective confidence intervals that are more similar?

Each box of Healthy Crunch breakfast cereal contains a coupon entitling you to a free package of garden seeds. At the Healthy Crunch home office, they use the weight of incoming mail to determine how many of their employees are to be assigned to collecting coupons and mailing out seed packages on a given day. (Healthy Crunch has a policy of answering all its mail on the day it is received.) Let x = weight of incoming mail and y = number of employees required to process the mail in one working day. A random sample of 8 days gave the following data.

In this setting we have Σx = 133, Σy = 79, Σx² = 2527, Σy² = 911, and Σxy = 1490.

(a) Find x, y, b, and the equation of the least-squares line. (Round your x and y to two decimal places. Round your least-squares estimates to four decimal places.)

(b) Draw a scatter diagram displaying the data. Graph the least-squares line on your scatter diagram. Be sure to plot the point (x, y).

(c) Find the sample correlation coefficient r and the coefficient of determination. (Round your answers to three decimal places.)

What percentage of variation in y is explained by the least-squares model? (Round your answer to one decimal place.)
%

(d) Test the claim that the population correlation coefficient ρ is positive at the 1% level of significance. (Round your test statistic to three decimal places.)

t =

Find or estimate the P-value of the test statistic.

P-value > 0.250

0.125 < P-value < 0.250

0.100 < P-value < 0.125

0.075 < P-value < 0.100

0.050 < P-value < 0.075

0.025 < P-value < 0.050

0.010 < P-value < 0.025

0.005 < P-value < 0.010

0.0005 < P-value < 0.005

P-value < 0.0005

Conclusion

Reject the null hypothesis, there is sufficient evidence that ρ > 0.

Reject the null hypothesis, there is insufficient evidence that ρ > 0.  

   Fail to reject the null hypothesis, there is sufficient evidence that ρ > 0.

Fail to reject the null hypothesis, there is insufficient evidence that ρ > 0.

(e) If Healthy Crunch receives 11 pounds of mail, how many employees should be assigned mail duty that day? (Round your answer to two decimal places.)

        employees

(f) Find S_e. (Round your answer to three decimal places.)
S_e =

(g) Find a 95% for the number of employees required to process mail for 11 pounds of mail. (Round your answer to two decimal places.)

(h) Test the claim that the slope β of the population least-squares line is positive at the 1% level of significance. (Round your test statistic to three decimal places.)

t =

Find or estimate the P-value of the test statistic.

P-value > 0.250

0.125 < P-value < 0.250    

0.100 < P-value < 0.125

0.075 < P-value < 0.100

0.050 < P-value < 0.075

0.025 < P-value < 0.050

0.010 < P-value < 0.025

0.005 < P-value < 0.010

0.0005 < P-value < 0.005

P-value < 0.0005

Conclusion

Reject the null hypothesis, there is sufficient evidence that β > 0.

Reject the null hypothesis, there is insufficient evidence that β > 0.  

Fail to reject the null hypothesis, there is sufficient evidence that β > 0.

Fail to reject the null hypothesis, there is insufficient evidence that β > 0.

(i) Find an 80% confidence interval for β and interpret its meaning. (Round your answers to three decimal places.)

Interpretation

For each additional pound of mail, the number of employees needed increases by an amount that falls within the confidence interval.

For each additional pound of mail, the number of employees needed increases by an amount that falls outside the confidence interval.

For each less pound of mail, the number of employees needed increases by an amount that falls within the confidence interval.

For each less pound of mail, the number of employees needed increases by an amount that falls outside the confidence interval.

1. Calculate the probabilities below using the following contingency table.

1. Probability that a mother in the study smoked during the pregnancy.
2. Probability that a mother smoked during the pregnancy if her education was below high school.
3. Probability that a mother smoked during pregnancy and had a college degree.
4. Probability that a mother smoked during pregnancy or that she graduated from college.
5. Probability that a mother did not smoke during her pregnancy given that she attended some college but did not have a degree.
6. Probability that a mother with some college smoked during pregnancy.

5. Suppose that in a city of 10,000 people, there are 4,000 who like football and 6,000 who do not. Suppose that we conduct a poll of 16 citizens. What is the probability that at least half of those polled like football? (Use Binomial approximation to find a decimal answer.) 1

6. Suppose that a random variable X is an Exponential Random Variable with parameter β = 3. (a) What is E(X)? (b) Compute P(X > 2). (c) Compute P(X > 5 | X > 3).

An accounting firm noticed that of the companies it audits, 85% show no inventory shortages, 10% show small inventory shortages, and 5% show large inventory shortages. The firm has devised a new accounting test for which it believes the following probabilities hold: P(company will pass test | no shortage) = .90 P(company will pass test | small shortage) = .50 P(company will pass test | large shortage) = .20

a. If a company being audited fails this test, what is the probability of a large or small inventory shortage?

b. If a company being audited passes this test, what is the probability of no inventory shortage?

A local college newsletter reported that the average American college student spends one hour​ (60 minutes) on a social media website daily. But you wonder if there is a difference between males and females. Attached below is a sample of 60 users of the website​ (30 males and 30​ females) and their recorded daily time spent on the website. Complete​ (a) and​ (b) below.

a. Assuming that the variances in the population of times spent on the website per day are​ equal, is there evidence of a difference in the mean time spent on the website per day between males and​ females? (Use a 0.05 level of​ significance.)

Let m1 be the mean daily time spent on the website for male college students and m2 be the mean daily time spent on the website for female college students. Determine the hypotheses. Choose the correct answer below.

Determine the test statistic.

Find the​ p-value.

Choose the correct conclusion below.

b. In addition to equal​ variances, what other assumption is necessary in​ (a)?

A. In addition to equal​ variances, it must be assumed that the samples are specifically chosen and not independently sampled.

B. In addition to equal​ variances, it must be assumed that the sample means are equal.

C.In addition to equal​ variances, no other assumptions must be made because the sample sizes are large enough ​(greater than or equals≥30 for each​ sample).Your answer is correct.

D. In addition to equal​ variances, it must be assumed that the population sizes are equal.

Let x be a random variable that represents white blood cell count per cubic milliliter of whole blood. Assume that x has a distribution that is approximately normal, with mean μ = 6450 and estimated standard deviation σ = 2400. A test result of x < 3500 is an indication of leukopenia. This indicates bone marrow depression that may be the result of a viral infection.

(a) What is the probability that, on a single test, x is less than 3500?

(b) What is the probability of x < 3500?

(c) Repeat part (b) for n = 3 tests taken a week apart. (Round your answer to four decimal places.)

When planning a date night, you have a choice of 2 types of restaurants: pizza (P) or barbeque (B); a choice of 4 types of movies: romantic comedy (R), action/adventure (A), drama (D), or foreign film (F); and a choice of 2 types of post-movie activities: grabbing coffee (C) or getting ice cream (I). If you are choosing only one of each, list the sample space in regard to the dates (combinations of restaurants, movies, and post-movie activities) you could pick from.

Separate the elements of the sample space with commas.

soft drink manufacturer wishes to know how many soft drinks adults drink each week. They want to construct a 98% confidence interval for the mean and are assuming that the population standard deviation for the number of soft drinks consumed each week is 1. The study found that for a sample of 898 adults the mean number of soft drinks consumed per week is 6.4. Construct the desired confidence interval. Round your answers to one decimal place. Lower and high endpoint

ment advisors recommend risk reduction through international diversification. International investing allows you to take advantage of the potential for growth in foreign economies, particularly in emerging markets. Janice Wong is considering investment in either Europe or Asia. She has studied these markets and believes that both markets will be influenced by the U.S. economy, which has a 19% chance for being good, a 48% chance for being fair, and a 33% chance for being poor. Probability distributions of the returns for these markets are given in the accompanying table.

a. Find the expected value and the standard deviation of returns in Europe and Asia. (Round intermediate calculations to at least 4 decimal places and final answers to 2 decimal places.)

b. What will Janice pick as an investment if she is risk neutral?

• Investment in Europe

• Investment in Asia