A study was conducted to determine the proportion of people who dream in black and white instead of color. Among 300 people over the age of​ 55, 65 dream in black and​ white, and among 297 people under the age of​ 25, 16 dream in black and white. Use a 0.05 significance level to test the claim that the proportion of people over 55 who dream in black and white is greater than the proportion for those under 25. Test the claim using a hypothesis test. Identify the test statistic. Identify the​ P-value. What is the conclusion based on the hypothesis​ test? Test the claim by constructing an appropriate confidence interval. What is the conclusion based on the confidence​ interval?

Suppose a mutual fund qualifies as having moderate risk if the standard deviation of its monthly rate of return is less than 66​%. A​ mutual-fund rating agency randomly selects 27 months and determines the rate of return for a certain fund. The standard deviation of the rate of return is computed to be 4.48​%. Is there sufficient evidence to conclude that the fund has moderate risk at the α=0.10 level of​ significance? A normal probability plot indicates that the monthly rates of return are normally distributed. What are the correct hypotheses for this​ test? Calculate the value of the test statistic. Use technology to determine the​ P-value for the test statistic. What is the correct conclusion at the α=0.10 level of​ significance?

You are the program officer for an outreach program for struggling families. Because of very limited funding (welcome to the non profit sector), you are only able to start the program up in zip codes with an average household income of less than $36,500.

Also because of limited funding, you rely on samples obtained by a government agency for each zipcode.

According to a sample of 800, zipcode 00001 has an average household of $39,500 with a standard deviation of $14,000. Using a confidence interval of 95%, is this zipcode immediately disqualified? Why or why not? Demonstrate your work.

The following table lists the weight of individuals before and after taking a diet prescribed by a weight-loss company for a month:

Weight-loss Data:

Individual: A, B, C, D, E, F

Weight Before (lb): 123.7, 128.7, 135.6, 194.9, 145.5, 162.3

Weight After (lb): 109.4, 109.7, 123.3, 186.5, 126.8, 151.5

Weight loss (lb): 14.3, 19.0, 12.3, 8.4, 18.7, 10.8

You may find this Student's t distribution table useful in answering the following questions. You may assume that the differences in weight are normally distributed.

a)Calculate the sample variance (sd2) of the changes in individual weights. Give your answer to 2 decimal places.

sd2 =

b)A disgruntled customer states: "This weight-loss company is a complete farce. All the people I know who signed up experienced no changes in their weight at all. I seriously doubt this diet has any effect whatsoever. I want my money back!"

You plan to do a hypothesis test on this claim where the hypotheses are:

H0: the customer's claim is true and the program has no effect on weight

HA: the customer's claim is not true and the program does have an effect on weight, whether it increases or decreases

According to the data given, you should accept, reject, or not reject the null hypothesis at a confidence level of 99%.

An education minister would like to know whether students at Gedrassi high school on average perform better at English or at Mathematics. Denoting by μ1 the mean score for all Gedrassi students in a standardized English exam and μ2 the mean score for all Gedrassi students in a standardized Mathematics exam, the minister would like to get a 95% confidence interval estimate for the difference between the means: μ1 - μ2.

A study was conducted where many students were given a standardized English exam and a standardized Mathematics exam and their pairs of scores were recorded. Unfortunately, most of the data has been misplaced and the minister only has access to scores for 4 students.

The populations of test scores are assumed to be normally distributed. The minister decides to construct the confidence interval with these 4 pairs of data points. This Student's t distribution table may assist you in answering the following questions.

a)Calculate the lower bound for the confidence interval. Give your answer to 3 decimal places.

Lower bound =

b)Calculate the upper bound for the confidence interval. Give your answer to 3 decimal places.

Upper bound =

An assistant claims that there is no difference between the average English score and the average Math score for a student at Gedrassi high school.

c)Based on the confidence interval the minister constructs, the claim by the assistant can or cannot be ruled out.

A two-variable model involving one quantitative explanatory variable and one categorical (binary) explanatory variable (and no interaction), results in two regression lines that are:

A.     Always parallel.

B.     Could be parallel but, depending on the data, may not.

C.      Never parallel.

D.     Always horizontal.

The two methods of including a binary categorical variable in a regression model are to use indicator coding or effect coding. For indicator coding in the two-variable model (with no interaction):

A.     The binary variable is coded (-1,1) and the coefficient for the binary variable in the corresponding regression equation is the difference between the two group means.

B.     The binary variable is coded (-1,1) and the coefficient for the binary variable in the corresponding regression equation is the difference between one of the group means and the least-squares mean (the overall mean).

C.      The binary variable is coded (0,1) and the coefficient coefficient for the binary variable in the corresponding regression equation is the difference between the two group means.

D.     The binary variable is coded (0,1) and the coefficient for the binary variable in the corresponding regression equation is the difference between one of the group means and the least-squares mean (the overall mean).

Chapter 6: Normal Probability (These problems are like the problems in Section 6.2). Using a Normal Distribution to find probabilities: Use the table E.2 in your text. Draw a sketch and indicate what probabilities (E.g. P (X<3 and X>10) for what is required for each part of the problem. To make sketches copy and paste into Word for the areas under the bell-curve you have the NormalSketch.ppt powerpoint slide in the Resources  Handout area on Laulima, The main point of providing a sketch is to give you a visual idea of what your solution will be. 2. Do problem (6 points) Remember, you need the sketches to get credit. You order and manage the medications in the Pharamacy for Queens hospital. The CEO is concerned because the hospital is ordering and stocking medicine with short shelf lives and its not being used and thrown away. There is a medicine called Harvoni that is used for Hepatitis the cost of a treatment is $95,000 and the shelf life for the medicine is 12 weeks. Last year s significant amount of this medicine was disposed because of the short shelf life: How many treatments should you order? For this question the mean (μ) was 20, the standard deviation (σ) was 5, skewness was .06 and kurtosis was - .27. a. You can find the probabilities for this problem assuming a normal (bell-shaped) curve. Why is it OK for this particular situation? b. What is the probability that you will use no more than10 treatments in a given week? c. What is the probability that will use more than 36 treatments in a given week? d. Would using more than 36 treatments in a week be an outlier for this data set? e. You expect touse μ harvoni each day. Because of the variability you will actually sell more or less each day. To understand this, find out how many less or more than μ you expect to sell 80% of the time. That is, find two values equal distance from the mean such that 80% of all values fall between them. Specifically find what number of x Harvoni where 80% of the values fall between μ-x and μ+x f. You can only have a fixed amount of amount of treatments on hand to sell every week. As in (e) you know you will surely use more or less than μ treatments each week. If you run out of treatments, your patients will die. But if you order too many treatments they will go bad and you will have to throw them out so you are willing to sell out occasionally. How many treatments must you have on hand to sell if you wanted to ensure you do not runl out more than 5% of the time? (This is called having a 95% service level) g. The z-value for having a given service level is called the safety-factor. Explain what this factor does in terms of μ and σ for the 95% service level you found in (f). What if you wanted to only have a 50% service level? What about 40% service level?

write as much you can*

Imagine that a group of obese children is recruited for a study in which their weight is measured, then they participate for 3 months in a program that encourages them to be more active, and finally their weight is measured again.

Explain how each of the following might affect the results:

regression to the mean

spontaneous remission

history

maturation

A random sample of 862 births included 434 boys. Use a 0.10 significance level to test the claim that 50.7​%

of newborn babies are boys. Do the results support the belief that 50.7​%

of newborn babies are​ boys? Identify the test statistic for this hypothesis test. Identify the​ P-value for this hypothesis test. Identify the conclusion for this hypothesis test.

he following question involves a standard deck of 52 playing cards. In such a deck of cards there are four suits of 13 cards each. The four suits are: hearts, diamonds, clubs, and spades. The 26 cards included in hearts and diamonds are red. The 26 cards included in clubs and spades are black. The 13 cards in each suit are: 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King, and Ace. This means there are four Aces, four Kings, four Queens, four 10s, etc., down to four 2s in each deck. You draw two cards from a standard deck of 52 cards without replacing the first one before drawing the second. (a) Are the outcomes on the two cards independent? Why? Yes. The events can occur together. Yes. The probability of drawing a specific second card is the same regardless of the identity of the first drawn card. No. The events cannot occur together. No. The probability of drawing a specific second card depends on the identity of the first card. (b) Find P(ace on 1st card and ten on 2nd). (Enter your answer as a fraction.) (c) Find P(ten on 1st card and ace on 2nd). (Enter your answer as a fraction.) (d) Find the probability of drawing an ace and a ten in either order. (Enter your answer as a fraction.)

A sample of 26 offshore oil workers took part in a simulated escape exercise, resulting in the accompanying data on time (sec) to complete the escape:

(a) Construct a stem-and-leaf display of the data. (Enter numbers from smallest to largest separated by spaces. Enter NONE for stems with no values.)

How does it suggest that the sample mean and median will compare?

The display is positively skewed, so the mean will be greater than the median. The display is negatively skewed, so the median will be greater than the mean.     The display is reasonably symmetric, so the mean and median will be close. The display is positively skewed, so the median will be greater than the mean. The display is negatively skewed, so the mean will be greater than the median.

(b) Calculate the values of the sample mean x and median x . [Hint: Σx_i = 9628.] (Round your answers to two decimal places.)

(c) By how much could the largest time, currently 423, be increased without affecting the value of the sample median? (Enter ∞ if there is no limit to the amount.)


By how much could this value be decreased without affecting the value of the sample median? (Enter ∞ if there is no limit to the amount.)


(d) What are the values of x and x when the observations are reexpressed in minutes? (Round your answers to two decimal places.)

1.

In the country of United States of Heightlandia, the height measurements of ten-year-old children are approximately normally distributed with a mean of 55.7 inches, and standard deviation of 1.7 inches.

What is the probability that the height of a randomly chosen child is between 53.05 and 53.95 inches? Do not round until you get your your final answer, and then round to 3 decimal places.

Answer= (Round your answer to 3 decimal places.)

2.

The mean daily production of a herd of cows is assumed to be normally distributed with a mean of 35 liters, and standard deviation of 4.2 liters.

A) What is the probability that daily production is less than 26.8 liters?

Answer= (Round your answer to 4 decimal places.)

B) What is the probability that daily production is more than 24.9 liters?

Answer= (Round your answer to 4 decimal places.)

Warning: Do not use the Z Normal Tables...they may not be accurate enough since WAMAP may look for more accuracy than comes from the table.

Find the critical value for a​ right-tailed test with

a=0.01

and

n=75.

The SAT has gone through many revisions over the years. People argue that female students generally do worse on math tests but better on writing tests. Consider the following portion of data on 20 students who took the SAT test last year. Information includes each student’s score on the writing and math sections of the exam, the student’s GPA, and a Female dummy variable that equals 1 if the student is female, 0 otherwise.

a-1. Estimate a linear regression model with math score as the response variable and GPA and the female dummy variable as the explanatory variables. (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.)

MathˆMath^ = _______ + _______ GPA + _____Female.

a-2. Compute the predicted math score for a male and female student with a GPA of 3.5. (Round coefficient estimates to at least 4 decimal places and final answer to 2 decimal places.)

The following weights in kilograms were recorded for a hockey team:
73 75 76 77 78 86 81 75 100 92 82 73 85 79
84 92 80 78 77 81 83 74 80 69 92 79 72 76
a) Find the mean, mode, and median weights.
b) Which of these three measures of central tendency is the least representative of the set of weights? Why?