Because not all airline passengers show up for their reserved seats, an airline sells 125 tickets for a flight that holds only 120 passengers. The proportion that a passenger does not show up is 10%, and the passengers behave independently. [Think Binomial Dist.]

a. What is the proportion that every passenger who shows up gets a seat?

b. What is the proportion that the flight departs with empty seats?

c. What are the mean and standard deviation of the number of passengers who show up?

Question 12

A simple random sample of 12 e-readers of a certain type had the following minutes of battery life.

287, 311, 262, 392, 313, 263, 293, 316, 286, 301, 287, 291

Assume that it is reasonable to believe that the population is approximately normal and the population standard deviation is 62. What is the upper bound of the 95% confidence interval for the battery life for all e-readers of this type?

Round your answer to one decimal places (for example: 319.4). Write only a number as your answer. Do not write any units.

Question 15

A random sample of 13 students were asked how long it took them to complete a certain exam. The mean length of time was 109.5 minutes, with a standard deviation of 68.2 minutes. Find the lower bound of the 90% confidence interval for the true mean length of time it would take for all students to complete the exam.

Round to one decimal place (for example: 108.1). Write only a number as your answer. Do not write any units.

Suppose you play a "daily number" lottery game in which three digits from 0–9 are selected at random, so your probability of winning is 1/1000. Also suppose lottery results are independent from day to day.

A. If you play every day for a 7-day week, what is the probability that you lose every day?

B. If you play every day for a 7-day week, what is the probability that you win at least once? (Hint: Make use of your answer to part a.)

C. Repeat parts a and b if you play every day for a 30-day month.

D. What if each digit can only be selected once. How many different ways can the three digits be selected?

E. If order does matter in the digits, how many different ways can the numbers be arranged?

A researcher is interested in finding a 98% confidence interval for the mean number of times per day that college students text. The study included 137 students who averaged 40.7 texts per day. The standard deviation was 13.4 texts. Round answers to 3 decimal places where possible. a. To compute the confidence interval use a distribution. b. With 98% confidence the population mean number of texts per day is between and texts. c. If many groups of 137 randomly selected members are studied, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population number of texts per day and about percent will not contain the true population mean number of texts per day.

Certified Behavior Analysts claim that their procedures are more effective than any other. Their procedures are clear-cut analytics that anyone can learn and apply. It’s not an art they proclaim, but a science. You decide to put it to test. You interview and survey the parents of autistic kids, loved ones of the depressed, and former sufferers of phobias, who had been treated with Behavior Therapy, Drug Therapy, and Play Therapy. Your survey generates a score from 1-100 with higher values indicating greater effectiveness of the therapy and 85 and above indicates complete resolution of the problem. Behavior Therapy: 58, 65, 71, 59, 81, 74, 83, 63 Drug Therapy: 59, 68, 32, 44, 38, 41, 30, 51 Play Therapy: 58, 61, 50, 60, 64, 62, 85, 57

1. Using the above data calculate the one-way analysis of variance in JASP. Report the F-ratio in APA style, including the p-value and eta-squared (treatment magnitude).

2. If the one-way ANOVA shows a significant difference among the groups, then calculate post hoc test to determine which groups are different – be sure you compare each group to each other group. Report the significant differences among the groups. If the one-way ANOVA does not show a significant difference, then state no difference.

The mean height of women in the United States (ages 20-29) is 64.2 inches with a standard deviation of 2.9 inches. A random sample of 60 women in this age group is selected. Assume that the distribution of these heights is normally distributed.

Are you more likely to randomly select 1 woman with a height more than 70 inches or are you more likely to select a random sample of 20 women with a mean height more than 70 inches? Show work necessary to answer this question: sketch both distributions and calculate each probability.

A) Sketch the distribution of women’s heights in the United States (age 20-29). Label the mean, label at least two standard deviations in each direction and shade the area in question. Calculate the probability that a randomly selected woman will have a height more than 70 inches. Show your work.

B) Sketch the sampling distribution of sample mean heights for random samples of 20 women in the United States (age 20-29). Label the mean, label at least two standard deviations in each direction and shade the area in question. Calculate the probability that a random sample of 20 women will have a mean height more than 70 inches. Show your work.

C) Which is more likely? Explain. Provide your answer as a sentence.

Directions: Complete the assignment. Clearly label each answer. Your answers for this assignment must include reasons; simply stating the answer without justification will earn partial credit. (32points)

1. The gestation period of gray squirrels in captivity is listed as 44 days. It is recognized that the potential life span of animals is rarely attained in nature, but the gestation period could be either shorter or longer. Suppose the gestation period of a random sample of 49 squirrels living in the wild is measured and the mean length of gestation time is 43 days. Test the hypothesis that squirrels living in the wild have the same gestation period as those in captivity at the 0.05 level of significance. Assume that σ = 6 days. Use the four step process for Hypothesis Testing. (8 points)

Step 1 – State Hypothesis in context of the problem.

Step 2 – Gather data, check assumptions, and find rejection region using α.

Step 3 – Calculate the appropriate test statistic and p-value.

Step 4 – State conclusion in context of the problem.

Step 1

Step 2

Step 3

Step 4

The following data represent the pH of rain for a random sample of 12 rain dates. A normal probability plot suggests the data could come from a population that is normally distributed. A boxplot indicates there are no outliers. Complete parts​ (a) through​ (d) below.

(a) Determine a point estimate for the population mean.

A point estimate for the population mean is ___. ​(Round to two decimal places as​ needed.)

(b) Construct and interpret a 95​% confidence interval for the mean pH of rainwater. Select the correct choice below and fill in the answer boxes to complete your choice. ​(Use ascending order. Round to two decimal places as​ needed.)

A. If repeated samples are​ taken, 95​% of them will have a sample pH of rain water between ___ and ___.

B. There is 95​% confidence that the population mean pH of rain water is between ___ and ___.

C. There is a 95​% probability that the true mean pH of rain water is between ___ and ___.

c) Construct and interpret a 99​% confidence interval for the mean pH of rainwater. Select the correct choice below and fill in the answer boxes to complete your choice. ​(Use ascending order. Round to two decimal places as​ needed.)

A. There is a 99​% probability that the true mean pH of rain water is between ____ and ___.

B. If repeated samples are​ taken, 99​% of them will have a sample pH of rain water between ____ and ___.

C. There is 99​% confidence that the population mean pH of rain water is between ____ and ____.

(d) What happens to the interval as the level of confidence is​ changed? Explain why this is a logical result. As the level of confidence​ increases, the width of the interval ____ This makes sense since ______

HERE IS THE GIVEN DATA

5.05
5.72
4.99
4.80
5.02
4.68
4.74
5.19
5.43
4.76
4.56
5.54

A famous problem in probability comes from the game show “Let’s Make a Deal.”  In it, a contestant is shown three doors.  Behind one door is a new car, and behind the other doors, there is nothing.  The contestant is asked to pick one of the three doors.  The host then opens up one of the two that was not chosen which always reveals that there is nothing behind that opened door.  The contestant is then asked if he or she would like to change their chosen door to the other unopened one.

A) Should he/she?  Explain why or why not. (Expresses opinion about whether the contestant should change his/her decision, and supports that opinion through sound application of the concepts of probability)

B) Can you think of another example where someone's intuition about probability may lead them down the wrong path?

The Law of Large Numbers is a statistical theory that you read about in this chapter. In your own words, what does this law say about the probability of an event? Perhaps you have also heard of something called the Law of Averages (also called the Gambler's Fallacy). Do an Internet search to find out additional information about both of these laws.

Are these the same laws? If not, how are they related and how are they different?

What general misconceptions do people have regarding these ideas?

A batter who had failed to get a hit in seven consecutive times at bat then hits a game-winning home run. When talking to reporters afterward, he says he was very confident that last time at bat because he knew he was "due for a hit."

In the late summer of 2008, a brief war broke out between the two countries—Russia and Georgia. Suppose you are a researcher interested in nationalistic attitudes in these two countries. You decided to use data from the World Values Survey, which is available at the following URL: http://www.worldvaluessurvey.org/. The data of interest are presented below on Russian respondents.

Exactly 940 persons between the ages of 15 and 29 indicated that they were “quite proud” of their nationality. Suppose for the moment that only 840 persons between the ages of 15 and 29 were “quite proud” of their nationality. Keeping the other cells as they were originally, recalculate the value of the chi-square statistic and determine whether it is statistically significant.

In order to estimate the difference between the MEAN yearly incomes of marketing managers in the East and West of the United States, the following information was gathered.

1. Develop an interval estimate for the difference between the MEAN yearly incomes of the marketing managers in the East and West. Use α = 0.05. Note that the population standard deviation is unknown, but the sample standard deviation is known. You will also need to calculate the degrees of freedom as shown on page 434 so that you can calculate t...
2. You will reuse a lot of what you did in the problem above. Use the p-value approach to conduct a full hypothesis test to determine if the MEAN yearly income of marketing managers in the East is significantly different from the West. p. 435 can help. Your difference in your formula is 0.

A carpet company advertises that it will deliver your carpet within 15 days of purchase. A sample of 49 past customers is taken. The average delivery time in the sample was 16.2 days. Assume the population standard deviation is known to be 5.6 days.

The annual profits for a company are given in the following table. Write the linear regression equation that represents this set of data, rounding all coefficients to the nearest ten-thousandth. Using this equation, estimate the year in which the profits would reach 413 thousand dollars.

Year (x)                Profits (y)

(in thousands of dollars)

1999 112

2000 160

2001 160

2002 173

2003 226

Can you please show step by step solution thanks.

Let’s supposed that we want to choose a random sample of library books. There are four ways we can choose the random sample. Based on descriptions given below, label each as either simple random, stratified random, cluster random, or systematic random .

a.The library books are storedon bookshelves. We number each bookshelf and use a random number generator to pick some bookshelves. All the books on the shelves that are picked will make up our random sample

.b.We first organized the books into two groups: fiction and non-fiction. We then number each fiction book and use a random number generator to pick some fiction books to be in our sample. We do the same for the non-fiction books.

c.We number each book and use a random number generator to pick books to be in our sample.d.We number each book and use a random number generator to pick one book. Then we will count off every 10thbook from that starting point to be in our sample.