Your authors present terms that are used in theory construction. Some of those terms are concepts, variables, statements and hypotheses. Explain how those words are related to one another.

Use a specific theory to illustrate the relationship. In other words, identify a theory; from that theory identify a concept and variables. From those variables develop a statement and a hypothesis.

A survey was conducted to determine, on average, how long patients have to wait to see a doctor. The number of patients that ended up waiting up to 2 hours to see a doctor, recorded in 10-minute intervals, is given in the table below.
a) Define and name the random variable associated with this data.
b) Find the probability distribution for the random variable and draw the corresponding histogram. Express all probabilities as a fraction in lowest terms.
c) What is the probability that a patient had to wait between 20 and 50 minutes?
d) What is the expected number of minutes a patient must wait? Give an exact answer. (2 marks

e) Calculate the standard deviation for this distribution. Explain what it means in the context of this problem.
2.

Waiting Time in minutes
10
20
30
40
50
60
70
80
90
100
110
120 Frequency of Occurrence
1
4
15
20
35
42
28
19
13
5
2
1
e) Calculate the standard deviation for this distribution. Explain what it means in the context of this problem.

Seedlings of the parasitic plant Cuscuta pentagona (dodder) hunt by directing growth preferentially toward nearby host plants. To investigate the possibility that the parasite detects volatile chemicals produced by host plants, a researcher placed individual dodder seedlings into a vial of water at the center of a circular paper disc. A chamber containing volatile extracts from tomato (a host plant) was placed at one edge of the disc, whereas a control chamber containing only solvent was placed at the opposite end. The researcher divided the disk in to 4, equal-area quadrats to record which direction the seedlings grew. 30 dodder plants were tested, and 17 grew toward the volatiles, 2 grew away from the volatiles (toward the solvent), 7 grew toward the left quadrant, and 4 grew toward the right quadrant.

1) Is this an experimental or observational study?

2) State null and alternative hypothesis

3) Which test is appropriate for this study? T-test, contingency test or goodness of fit?

According to the “Bottled Water Trends for 2014” report (bit.ly/1gx5ub8), the U.S. per capita consumption of bottled water in 2013 was 31.8 gallons. Assume that the per capita consumption of bottled water in the United States is approximately normally distributed with a mean of 31.8 gallons and a standard deviation of 10 gallons.

PLEASE USE NORMDIST AND NORMINV IN EXCEL

a. What is the probability that someone in the United States con- sumed more than 32 gallons of bottled water in 2013?

b. What is the probability that someone in the United States consumed between 10 and 20 gallons of bottled water in 2013?

c. What is the probability that someone in the United States consumed less than 10 gallons of bottled water in 2013?

d. Ninety-nine percent of the people in the United States consumed less than how many gallons of bottled water?

e) The amount of water consumed by 92% of US population will be between what two values symmetrically distributed around the mean?

Most companies have increased their dependence on computers and software. As a result, more employee time is spent on the telephone with technical support for the software. A sample of 8 times spent on the phone with technical support yielded the following data:

Construct a 98 percent confidence interval estimate of the true mean population time that is spent by employees on the telephone with technical support for the software. Use only the appropriate formula and/or statistical table in your textbook to answer this question. Negative values should be indicated by a minus sign. Report your answers to 2 decimal places, using conventional rounding rules.

Answer: $ _____≤ (Click to select) ≤ $____

#1 Assume that a new interpretation of the frustration aggression hypothesis says that it is not all people who become aggressive when frustrated, but only those who have been brought up in a home where physical punishment is used become aggressive when frustrated. To test this hypothesis, two groups of children are found. One group is brought up in homes where physical punishment is used as a form of discipline. The other group consists of children whose parents chastise them verbally, or remove privileges, but do not actually hit them. The children are all placed in a situation where they are frustrated in the course of play activity. The play situation includes a doll that the children have in their hands at the time of the frustration experience. The experimenter intends to have judges classify the children as either physically aggressive or not, physically aggressive toward the doll (at the time of frustration). Which statistic would be used?

#2 A chi-square test for goodness of fit is used to examine the distribution of individuals across three categories, and a chi-square test for independence is used to examine the distribution of individuals in a 2×3 matrix of categories. Which test has the larger value for df?

#3 A chi-square test for independence is being used to evaluate the relationship between two variables. If the test has df = 2, what can you conclude about the two variables?

#4 Under what circumstances will the chi-square test for goodness of fit produce a large value for the chi-square?

#5 For the chi-square test for goodness of fit, the researcher must select a sample with an equal number of individuals in each category.

True

False

#6 A chi-square test for goodness of fit is used to examine the distribution of individuals across three categories, and a chi-square test for independence is used to examine the distribution of individuals in a 2×2 matrix of categories. Which test has the larger value for df?

#7 What is referred to by the term expected frequencies?

#8 The observed frequencies for a chi-square test can be fractions or decimal values.

True

False

#9 The expected frequencies for a chi-square test are always whole numbers (no fractions or decimals).

True

False

#10 For a chi-square test, the observed frequencies are obtained from the sample.

True

False

#11 A researcher used a sample of n = 60 individuals to determine whether there are any preferences among four brands of pizza. Each individual tastes all four brands and selects his/her favorite. If the data are evaluated with a chi-square test for goodness of fit using α = .05, then how large does the chi-square statistic need to be to reject the null hypothesis?

#12 In general, a large value for chi-square indicates a good fit between the sample data and the null hypothesis.

True

False

#13 A chi-square test for independence is used to evaluate the relationship between two variables. If both variables are classified into 2 categories, then what is the df value for the chi-square statistic?

#14 For the expected frequencies in a chi-square test for independence, the proportions for any row are the same as the proportions in every other row.

True

False

#15 ​ Which of the following best describes the possible values for a chi-square statistic?

Ten females were divided into two equal groups. One group was taught how to concentrate on their breathing (a breathing meditation). A second group was told to imagine that the day was very hot and that they would be allowed to place their hand in cool water. Both groups placed their right hand in buckets of ice water for three minutes. Afterward, they rated their pain on a scale of one to seven (with seven meaning intense pain). Analyze the data and conclude whether the any of the methods was effective in reducing pain.

A. What is the dependent variable?
B. What is the null and alternate hypothesis?
C. Calculate t and note the critical values
D. Calculate d
E. Write your results and interpretations with appropriate stat notations.

Breathing Meditation       Imagination

                             3                         4

                             2                         5

                             4                         7

                             3                         6

                             2                         6

At a certain coffee​ shop, all the customers buy a cup of coffee and some also buy a doughnut. The shop owner believes that the number of cups he sells each day is normally distributed with a mean of 330 cups and a standard deviation of 23 cups. He also believes that the number of doughnuts he sells each day is independent of the coffee sales and is normally distributed with a mean of 170 doughnuts and a standard deviation of 13. Complete parts​ a) through​ c).

Question: The shop is open every day but Sunday. Assuming​ day-to-day sales are​ independent, what's the probability​ he'll sell over 2000 cups of coffee in a​ week? _____________ (round to three decimals as needed.)

Question: Whats the probability that on any given day he'll sell a doughnut to more than half of his coffee customers ? ___________ (round to three decimal places as needed).

A. The data below represent a random sample of 9 scores on a statistics quiz. (The maximum possible score on the quiz is 10.) Assume that the scores are normally distributed with a standard deviation of 1.6. Estimate the population mean with 93% confidence. 6,10,6,4,5,7,2,9,6 6 , 10 , 6 , 4 , 5 , 7 , 2 , 9 , 6 Note: For each confidence interval, enter your answer in the form (LCL, UCL). You must include the parentheses and the comma between the confidence limits.

Confidence Interval =

B. Among the most exciting aspects of a university professor's life are the departmental meetings where such critical issues as the color the walls will be painted and who gets a new desk are decided. A sample of 20 professors was asked how many hours per year are devoted to such meetings. The responses are listed below. Assuming that the variable is normally distributed with a standard deviation of 6 hours, estimate the mean number of hours spent at departmental meetings by all professors. Use a confidence level of 90%.

7,11,11,10,17,5,4,9,19,14,4,1,22,10,15,21,17,3,18,16

Note: For each confidence interval, enter your answer in the form (LCL, UCL). You must include the parentheses and the comma between the confidence limits.

Confidence Interval =

The daily exchange rates for the​ five-year period 2003 to 2008 between currency A and currency B are well modeled by a normal distribution with mean 1.814 in currency A​ (to currency​ B) and standard deviation 0.035 in currency A. Given this​ model, and using the​ 68-95-99.7 rule to approximate the probabilities rather than using technology to find the values more​ precisely, complete parts​ (a) through​ (d).

Question: ​a) What would the cutoff rate be that would separate the highest 2.5​% of currency​ A/currency B​ rates? The cutoff rate would be ___________ (type an integer or a decimal rounded to the nearest thousandth as needed)

Question: What would the cutoff rate be that would separate the highest 50% ? The cutoff rate would be _______________

Question: What would the cutoff rate be that would separate the middle 68% ? The lower cutoff rate would be ____________

Question: The upper cutoff rate would be ? ____________________

Question: What would the cutoff rate be that would separate the highest 16%? ________________

A building contractor buys 80% of his cement from supplier A and 20​% from supplier B. A total of 75​% of the bags from A arrive​ undamaged, while 85​% of the bags from B arrive undamaged. Find the probability that a damaged bag is from supplier Upper A.

It is common wisdom that death of a spouse can lead to health deterioration of the partner left behind. Is common wisdom right or wrong in this case? To investigate, Maddison and Viola (1968) measured the degree of health deterioration of 132 widows in the Boston area, all of whose husbands had died at the age of 45-60 within a fixed six-month period before the study. A total of 28 of the 132 widows had experienced a marked deterioration in health, 47 had seen a moderate deterioration, and 57 had seen no deterioration in health.Of 98 control women with similar characteristics who had not lost their husbands, 7 saw a marked deterioration in health over the same time period, 31 experienced a moderate deterioration of health, and 60 saw no deterioration.

1) Is this study observational or experimental?

2) State the null and alternative hypothesis

3) Which appropriate statistical test would be done for this experiment? Contingency analysis, t-test or goodness of fit?

The owner of a local golf course wants to examine the difference between the average ages of males and females that play on the golf course. Specifically, he wants to test if the average age of males is greater than the average age of females. If the owner conducts a hypothesis test for two independent samples and calculates a p-value of 0.5441, what is the appropriate conclusion? Label males as group 1 and females as group 2.

You are looking for a way to incentivize the sales reps that you are in charge of. You design an incentive plan as a way to help increase in their sales. To evaluate this innovative plan, you take a random sample of your reps, and their weekly incomes before and after the plan were recorded. You calculate the difference in income as (after incentive plan - before incentive plan). You perform a paired samples t-test with the following hypotheses: Null Hypothesis: μ_D ≥ 0, Alternative Hypothesis: μ_D< 0. You calculate a p-value of 0.001. What is the appropriate conclusion of your test?

It is reported in USA Today that the average flight cost nationwide is $468. You have never paid close to that amount and you want to perform a hypothesis test that the true average is actually different from $468. The hypotheses for this situation are as follows: Null Hypothesis: μ = 468, Alternative Hypothesis: μ ≠ 468. If the true average flight cost nationwide is $468 and the null hypothesis is rejected, did a type I, type II, or no error occur?

1. a There is a 50% chance of thunderstorms on Monday, a 50% chance on Tuesday and a 50% chance on Wednesday. Assume these are independent events. What is the probability that there will be thunderstorms on Monday, Tuesday, and Wednesday? Show your work.   b) A student says that if P(A) = P(A|B), then A and B must be independent events. Is the student correct? Explain.  Give a real life example that can be represented by P(A) = P(A|B). c) Describe the relationship between a change in the sample size and the chance in the margin of error.d) Describe a situation with a 20% probability of success in each of 4 trials. Graph the binomial distribution. e) On a math test the mean score is 82 with a standard deviation of 3. A passing score is 70 or greater. Choose a passing score that you would consider to be the outlier. Justify your choice.