A European growth mutual fund specializes in stocks from the British Isles, continental Europe, and Scandinavia. The fund has over 375 stocks. Let x be a random variable that represents the monthly percentage return for this fund. Suppose x has mean μ = 1.2% and standard deviation σ = 0.5%.

(a) Let's consider the monthly return of the stocks in the fund to be a sample from the population of monthly returns of all European stocks. Is it reasonable to assume that x (the average monthly return on the 375 stocks in the fund) has a distribution that is approximately normal? Explain. , x is a mean of a sample of n = 375 stocks. By the , the x distribution approximately normal.

(b) After 9 months, what is the probability that the average monthly percentage return x will be between 1% and 2%? (Round your answer to four decimal places.)

(c) After 18 months, what is the probability that the average monthly percentage return x will be between 1% and 2%? (Round your answer to four decimal places.)

(d) Compare your answers to parts (b) and (c). Did the probability increase as n (number of months) increased? Why would this happen?

Yes, probability increases as the mean increases.

Yes, probability increases as the standard deviation decreases.

No, the probability stayed the same.

Yes, probability increases as the standard deviation increases.

(e) If after 18 months the average monthly percentage return x is more than 2%, would that tend to shake your confidence in the statement that μ = 1.2%? If this happened, do you think the European stock market might be heating up? (Round your answer to four decimal places.)

P(x > 2%) = ?????

Explain. This is very likely if μ = 1.2%. One would suspect that the European stock market may be heating up.

This is very likely if μ = 1.2%. One would not suspect that the European stock market may be heating up.

This is very unlikely if μ = 1.2%. One would not suspect that the European stock market may be heating up.

This is very unlikely if μ = 1.2%. One would suspect that the European stock market may be heating up.

You are interested in determining whether an experimental birth control pull has the side effects of changing blood pressure. You plan to randomly sample 18 women from the city in which you live. You give half of them a placebo for a month and then measure their diastolic blood pressure. Then you switch them to the birth control pill for a month and again measure their blood pressure. The other 9 women receive the same treatment except they are given the birth control pill first for a month, followed by the placebo for a month. The blood pressure readings are shown here. What is the power of your study to reject the null assuming that the alternative hypothesis is true. Assume alpha =.05 non directional alternative hypothesis. YOU DO NOT NEED ANY DATA IT ONLY LOOKS FOR POWER

What is the power to detect a false null hypothesis assuming Preal=.9. Put your work and answer below.

What is the probability of failing to reject the null if the null is false assuming Preal =.9. Put your work and answer below.

What is the power to detect a false null hypothesis assuming Preal=.7. Put your work and answer below.

What is the probability of making a type 2 error assuming Preal =.7. Put your work and answer below.

The following data represent petal lengths (in cm) for independent random samples of two species of Iris. Petal length (in cm) of Iris virginica: x1; n1 =

35 5.1 5.8 6.5 6.1 5.1 5.5 5.3 5.5 6.9 5.0 4.9 6.0 4.8 6.1 5.6 5.1 5.6 4.8 5.4 5.1 5.1 5.9 5.2 5.7 5.4 4.5 6.4 5.3 5.5 6.7 5.7 4.9 4.8 5.9 5.1

Petal length (in cm) of Iris setosa: x2; n2 =

38 1.6 1.8 1.4 1.5 1.5 1.6 1.4 1.1 1.2 1.4 1.7 1.0 1.7 1.9 1.6 1.4 1.5 1.4 1.2 1.3 1.5 1.3 1.6 1.9 1.4 1.6 1.5 1.4 1.6 1.2 1.9 1.5 1.6 1.4 1.3 1.7 1.5 1.6

(a) Use a calculator with mean and standard deviation keys to calculate x1, s1, x2, and s2. (Round your answers to two decimal places.)

x1 =

s1 =

x2 =

s2 =

(b) Let μ1 be the population mean for x1 and let μ2 be the population mean for x2. Find a 99% confidence interval for μ1 − μ2. (Round your answers to two decimal places.)

lower limit

upper limit

(c) Explain what the confidence interval means in the context of this problem. Does the interval consist of numbers that are all positive? all negative? of different signs? At the 99% level of confidence, is the population mean petal length of Iris virginica longer than that of Iris setosa?

Because the interval contains only positive numbers, we can say that the mean petal length of Iris virginica is longer.

Because the interval contains only negative numbers, we can say that the mean petal length of Iris virginica is shorter.   

Because the interval contains both positive and negative numbers, we cannot say that the mean petal length of Iris virginica is longer.

(d) Which distribution did you use? Why?

The Student's t-distribution was used because σ₁ and σ₂ are unknown.

The standard normal distribution was used because σ₁ and σ₂ are unknown.

The Student's t-distribution was used because σ₁ and σ₂ are known.

The standard normal distribution was used because σ₁ and σ₂ are known.

Do you need information about the petal length distributions? Explain.

Both samples are large, so information about the distributions is not needed

.Both samples are large, so information about the distributions is needed.

Both samples are small, so information about the distributions is needed.

Both samples are small, so information about the distributions is not needed.

​If, based on a sample size of 850​, a political candidate finds that 471 people would vote for him in a​ two-person race.

a. A 90% confidence interval for his expected proportion of the vote is ____ , ____

b. Would he be confident of winning based on this​ poll?

A. How well do people remember their past diet? Data are available for 91 people who were asked about their diet when they were 18 years old. Researchers asked them at about age 55 to describe their eating habits at age 18. For each subject, the researchers calculated the correlation between actual intakes of many foods at age 18 and the intakes the subjects now remember. The median of the 91 correlations was r = 0.217. The researchers stated, "We conclude that memory of food intake in the distant past is fair to poor".

Choose the best reason why r = 0.217 points to this conclusion.

Because a correlation of 0.217 indicates a negative association.

Because a correlation of 0.217 indicates a positive association.

Because a correlation of 0.217 indicates a strong association.

Because a correlation of 0.217 indicates a weak association.

Because a correlation of 0.217 indicates no association.

B. Although research questions usually concern a _________, the actual research is typically conducted with a ________.

sample, statistic

population, parameter

sample, population

population, sample

What is the model for this linear programing problem?

USA Today reported that approximately 25% of all state prison inmates released on parole become repeat offenders while on parole. Suppose the parole board is examining five prisoners up for parole. Let x = number of prisoners out of five on parole who become repeat offenders. x 0 1 2 3 4 5 P(x) 0.217 0.368 0.220 0.156 0.038 0.001 (a) Find the probability that one or more of the five parolees will be repeat offenders. (Round your answer to three decimal places.) Incorrect: Your answer is incorrect. How does this number relate to the probability that none of the parolees will be repeat offenders? These probabilities are the same. This is twice the probability of no repeat offenders. This is five times the probability of no repeat offenders. This is the complement of the probability of no repeat offenders. These probabilities are not related to each other. (b) Find the probability that two or more of the five parolees will be repeat offenders. (Round your answer to three decimal places.) (c) Find the probability that four or more of the five parolees will be repeat offenders. (Round your answer to three decimal places.) (d) Compute μ, the expected number of repeat offenders out of five. (Round your answer to three decimal places.) μ = prisoners (e) Compute σ, the standard deviation of the number of repeat offenders out of five. (Round your answer to two decimal places.) σ = prisoners

The manufacturers of Good-O use two different types of machines to fill their 25 kg packs of dried dog food. On the basis of random samples of size 15 and 18 from output from machines 1 and 2 respectively, the mean and standard deviation of the weight of the packs of dog food produced were found to be 28.99 kg and 0.142 kg for machine 1 and 26.376 kg and 0.383 kg for machine 2. Hence, under the usual assumptions, determine a 95% confidence interval for the difference between the average weight of the output of machine 1 and machine 2. Use machine 1 minus machine 2, stating the upper limit of the interval correct to three decimal places.

5. Describe what we know about the theoretical distribution of sample means. Be sure to

include answers to the questions that follow:



What is a distribution of sample means? How is this different from the

distributions we have been working with up through Chapter 6?



According to the Central Limit Theorem, what three things do we know about

the theoretical distribution of sample means?



Define standard error.



In your own words, what does standard error tell us and why do we need this

information?



How is standard error different from standard deviation?

A facility has a waste storage tank with a capacity of 40 cubic feet. Each week the tank produces either 0, 10, 20, or 30 cubic feet of waste with respective probabilities of 0.1, 0.4, 0.3, and 0.2. If the amount of waste produced in a week creates a situation where the tank would overflow, the amount exceeding the tank’s capacity can be removed at a cost of $3 per cubic foot. At the end of each week, a contracted service is available to remove waste. The service costs $40 for each visit plus $1 per cubic foot of waste removed. The facility manager decides to adopt a policy where, if the tank contains more than 20 cubic feet of waste, the contract service comes at the end of the week and removes all of the waste in the tank. Otherwise, the service does not come, and no waste is removed. Model the amount of waste in the tank as a Markov chain. Pay particular attention to when (at what point in the week) the amount of waste is measured or recorded

A study was done to explore the number of chocolate bars consumed by 16-year-old girls in a month's time. The results are shown below. Number of Chocolate Bars Consumed 56 46 12 62 39 24 59 51 39 52 28 41 10 64 27 0 34 5 55 32 42 24 14 63 1 63 52 58 52 26 Use the data from the chocolate bar study to answer the following questions. Use SPSS for all calculations. Copy and paste the SPSS output into the word document, highlighting the correct answer. Additionally, type the correct answer into your word document next to the corresponding question. 1. Identify the level of measurement used in this study. 2. Using SPSS, run descriptive statistics on the data: a. Find the mean, median, and mode of the number of chocolate bars consumed by 16-year-old girls in a month. b. Find the variance and standard deviation of the number of chocolate bars consumed by 16-year-old girls in a month. 3. Create a frequency distribution table with six intervals/classes. 4. Create a histogram based on the Frequency table in problem 3.

An ANOVA table for a one-way experiment gives the following:

Source df SS

Between factors 2 810

Within (error) 8 720

Answer true or false and explain for the following six statements:

The null hypothesis is that all four means are equal.

The calculated value of F is 4.500.

The critical value for F for 5% significance is 6.06.

The null hypothesis cannot be rejected at 5% significance.

The null hypothesis cannot be rejected at 1% significance.

There are 10 observations in the experiment.

7.20 Body measurements, Part III. Exercise 7.13 introduces data on shoulder girth and height of a group of individuals. The mean shoulder girth is 107.30 cm with a standard deviation of 10.34 cm. The mean height is 171.14 cm with a standard deviation of 9.41 cm. The correlation between height and shoulder girth is 0.69. 1. (a) Write the equation of the regression line for predicting height. 2. (b) Interpret the slope and the intercept in this context. 3. (c) Calculate R2 of the regression line for predicting height from shoulder girth, and interpret it in the context of the application. 4. (d) A randomly selected student from your class has a shoulder girth of 100 cm. Predict the height of this student using the model. 5. (e) The student from part (d) is 160 cm tall. Calculate the residual, and explain what this residual means. 6. (f) A one year old has a shoulder girth of 56 cm. Would it be appropriate to use this linear model to predict the height of this child? *answers to 3 decimal points*!!!

Roll two ordinary dice and let X be their sum. Draw the pmf and cmf for X. Compute the mean and standard deviation of X. Solve using R studio coding.

Suppose there is a basket containing one apple and two oranges. A student randomly pick one fruit from the basket until the first time the apple is picked. (Sampling with replacement)

(a) What is the sample space for this experiment? What is the probability that the student pick the apple after i tosses?

(b) What is the expected number of times the students need to pick the apple?

(c) Let E be the event that the first time an apple is picked up is after an even number of picks. What set of outcomes belong to this event? What is the probability that E occurs?