We wish to estimate what percent of adult residents in a certain county are parents. Out of 500 adult residents sampled, 215 had kids. Based on this, construct a 95% confidence interval for the proportion pp of adult residents who are parents in this county.

Give your answers as decimals, to three places.

< pp <

To study the effect of temperature on yield in a chemical process, five batches were produced at each of three temperature levels. The results follow.

a. Construct an analysis of variance table (to 2 decimals but p-value to 4 decimals, if necessary).

b. Use a  level of significance to test whether the temperature level has an effect on the mean yield of the process.

Calculate the value of the test statistic (to 2 decimals).

The -value is - Select your answer

-less than .01between .01 and .025between .025 and .05between .05 and .10greater than .10Item 12

What is your conclusion?

- Select your answer

-Conclude that the mean yields for the three temperatures are not all equalDo not reject the assumption that the mean yields for the three temperatures are equalItem 13

Problem 2 (20 pts). Hypothesis testing - Imagine a study designed to test whether daughters resemble their fathers. In each trial of the study, a participant examines a photo of one girl and photos of two adult men, one of whom is girl's father. The participant must guess is the father. If there is no daughter-father resemblance, then the probability that the participant guesses correctly is only 1/2. Possible-meaningful hypotheses are: Ho: Participants pick the father correctly half the time HA: Participants pick the father correctly more frequently than half the time. (a) Assume that 13 out of 18 participants correctly guessed the father of the daughter. Test the null hypothesis Ho. Calculate the P-value and compare it with the standard significance level (a = 0.05). Will you reject Ho? (b) Assume that 12 out of 18 were correct. Will you reject Ho? (C) Assume that 12 x 2 = 24 out of 18 x 2 = 36 were correct. Will you reject Ho? (d) How/why are your answers in (b) and (c) different? Caution: Examine carefully if this is a one-sided or two-sided test.

The table below gives the completion percentage and interception percentage for five randomly selected NFL quarterbacks. Based on this data, consider the equation of the regression line, y^=b0+b1x, for using the completion percentage to predict the interception percentage for an NFL quarterback. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant.

a) Find the estimated slope. Round your answer to three decimal places.

b) Find the estimated y-intercept. Round your answer to three decimal places.

c) Determine if the statement "All points predicted by the linear model fall on the same line" is true or false.

d) Find the estimated value of y when x=55.9. Round your answer to three decimal places.

e) According to the estimated linear model, if the value of the independent variable is increased by one unit, then the change in the dependent variable y^ is given by?

f) Find the value of the coefficient of determination. Round your answer to three decimal places.

The following table lists the activities needed to complete a project. The first column lists the activities and the “follows” column shows which other activity or activities, (if any), must be completed before these activities can start. The remaining columns give three estimates of the activity duration; the mean duration calculated from these estimates and standard deviation assuming a beta distribution of activity duration.

e) What is the probability that the project will be completed between 38 and 45 days? Show your workings! (4 points)
  
f) Answer the project manager’s question:
“I want to tell the client a project length which I am 89.97% sure that we can meet _- What figure should I give them?" (4 points)

The wind speed in Laramie, Wyoming is normally distributed. The average wind speed for the state of Wyoming is approximately 20 mph. A curious student wanted to find out if the wind speed in Laramie was different than the state average. They took a sample of 25 random days in Laramie, measured the wind speed, and found an average of 18 mph with a standard deviation of 7.8 miles per hour.

Test the claim that the average wind speed in Laramie is less than the state average. Provide all six steps to the hypothesis test, using both a critical value AND a p-value to make your decision about the null.

Provide the confidence interval estimate of the true wind speed in Laramie.

Explain how your hypothesis test in 8_1 and your confidence interval in 8_2 are consistent.

A manager of an e-commerce company would like to determine average delivery time of the products. A sample of 25 customers is taken. The average delivery time in the sample was four days with a standard deviation of 1.2 days. Suppose the delivery times are normally distributed.

1. Provide a 95 % confidence interval for the mean delivery time.
2. The manager claims that the average delivery time of their products does not exceed 3 days. Write the null and alternative hypothesis regarding to the claim of  the manager.
3. Test the manager’s claim at 95 % confidence level.

For an effective parental skill study, a researcher asked: How many hours do your kids watch the television during a typical week in Barcelona? The mean of 100 Kids (ages 6-11) spend about 28 hours a week in front of the TV. Suppose the study follows a normal distribution with standard deviation 5.

1. Estimate the mean of all kids (ages 6-11) in Barcelona, using 99% confidence interval. (show all the calculations)
2. Write the conclusion of your result

A random sample of 124 women over the age of 15 found that 3.68% of them have been divorced. A random sample of 290 men over the age of 15 found that 5.86% have been divorced. Assuming normality and using a 95% significance level, test the claim that the proportion of divorced women is different than the proportion of divorced men.

For this scenario, provide a hypothesis test with all six steps and provide both the critical value and the p-value.

provide a confidence interval estimate of the true difference in proportions between men and women who have been divorced.   

Explain how your hypothesis test in 12 and your confidence interval in 13 are consistent.

A Shopping Mall sells trays of eggs of which some are returned because they are defective and it has been observed that 15% of the trays are defectives. The defective and no defective trays where observed on a random manner. If 8 trays are randomly collected, Find :-

a) The probability that exactly 2 of them are defective

b) The probability that at least 3 are defective

c) The probability that at most 2 are defective

d) The probability that no tray is defective

1. In an influenza outbreak, you learn that in a factory 13 of 52 men workers were ill. 25 of 52 women workers were ill. Using a hand-calculated chi-square test, determine whether the difference between men and women in illness attack rate is significant. Show your work and answer here.

Type T (for True) or F (for False) for each statement for both Discrete and Continuous random variables.

Question 16) X cannot map the same sample point to two different numbers. Discrete: Continuous:

Question 17) The sample space (domain) must be discrete. Discrete: Continuous:

Question 18 ) The range of X is uncountably infinite. Discrete: Continuous:

Question 19) The area under the F(x) function is 1. Discrete: Continuous:

Question 20) The cdf F(x) is differentiable everywhere. Discrete: Continuous:

Question 21) There exists a point y so that the cdf F(x) = 0 for all x ≤ y. Discrete: Continuous:

Question 22 ) The pf/pdf f(x) is non-decreasing. Discrete: Continuous:

Question 23) The pf/pdf f(x) is differentiable everywhere. Discrete: Continuous:

Question 24) E[X2] = Var(X) + (E[X])2. Discrete: Continuous:

Question 25) A symmetric distribution has mean equal to the midpoint of the range. Discrete: Continuous:

In one paragraph of 5 to 8 sentence, describe/explain how the normal distribution may be used or applied in your own life (career, home life, hobby, etc.).



As part of your description/explanation of how the normal distribution may be used or applied in your own life, include an applicable example in description/explanation.

An educational psychologist studies the effect of frequent testing on retention of class material. In one of the professor's sections, students are given quizzes each week. The second section receives only two tests during the semester. At the end of the semester, both sections receive the same final exam, and the scores are summarized below.

a. Do the data indicate that testing frequency has a significant effect on performance? Use a two-tailed test with α = .01. (7 points)

b. Compute r2 and state the size of the effect (e.g. small, medium, large). (2 points)

Frequent Quizzes n=15,m=72,SS=112

two exams n=15,M=68,SS=98

Education influences attitude and lifestyle. Differences in education are a big factor in the "generation gap." Is the younger generation really better educated? Large surveys of people age 65 and older were taken in n₁ = 38 U.S. cities. The sample mean for these cities showed that x₁ = 15.2% of the older adults had attended college. Large surveys of young adults (age 25 - 34) were taken in n₂ = 34 U.S. cities. The sample mean for these cities showed that x₂ = 18.1% of the young adults had attended college. From previous studies, it is known that σ₁ = 7.2% and σ₂ = 5.4%. Does this information indicate that the population mean percentage of young adults who attended college is higher? Use α = 0.05.

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: μ₁ = μ₂; H₁: μ₁ > μ₂H₀: μ₁ < μ₂; H₁: μ₁ = μ₂     H₀: μ₁ = μ₂; H₁: μ₁ ≠ μ₂H₀: μ₁ = μ₂; H₁: μ₁ < μ₂

(b) What sampling distribution will you use? What assumptions are you making?

The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations.The standard normal. We assume that both population distributions are approximately normal with known standard deviations.     The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations.The Student's t. We assume that both population distributions are approximately normal with known standard deviations.

What is the value of the sample test statistic? (Test the difference μ₁ − μ₂. Round your answer to two decimal places.)


(c) Find (or estimate) the P-value. (Round your answer to four decimal places.)


Sketch the sampling distribution and show the area corresponding to the P-value.

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?

At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.     At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(e) Interpret your conclusion in the context of the application.

Fail to reject the null hypothesis, there is insufficient evidence that the mean percentage of young adults who attend college is higher.Reject the null hypothesis, there is sufficient evidence that the mean percentage of young adults who attend college is higher.     Fail to reject the null hypothesis, there is sufficient evidence that the mean percentage of young adults who attend college is higher.Reject the null hypothesis, there is insufficient evidence that the mean percentage of young adults who attend college is higher.