Snow Geese lay 4 eggs in a nest. A field biologist wanted to know if there is a relationship between the order in which the eggs are laid and the sex of each egg. Please see the table below.

Is there a relationship between sex and laying order in snow geese?

1. What are the null and alternate hypotheses for the chi-square goodness of fit test?

2. What are the expected counts under the null hypothesis?

3. Use Minitab to determine a chi-square test statistic and P value

4. Do you accept or reject the null?

You are interested in investing in two different shares. The anticipated annual return for a $1,000 investment in each share under different economic conditions is given below, together with the probability that each of these economic conditions will occur.

1. Calculate the expected return for share X and for share Y.

2. Calculate the standard deviation for share X and for share Y.

3. Would you invest $1000 in share X or share Y or are they both equally desirable? Give a broad explanation of your answer.

Are beer, wine, and liquor consumed equally by Americans? A random sample found that out of 647 people, 293 selected beer, 218 selected wine, and 136 selected liquor.

1. What are the null and alternate hypotheses for the chi-square goodness of fit test?

2. What are the expected counts under the null hypothesis?

3. Determine a chi-square test statistic and P value

4. Do you accept or reject the null?

Mendel crossed pea plants that had yellow-round seeds with plants that had green-wrinkled seeds. The first generation produced plants with all yellow-round seeds. Self crossing of these plants produced the following F2 phenotypes:

The expected phenotypic ratio is 9:3:3:1

1. What are the null and alternate hypotheses for the chi-square goodness of fit test?

2. What are the expected counts under the null hypothesis?

3. Determine a chi-square test statistic and P value

4. Do you accept or reject the null?

You collect data to answer the research question, “Are high school boys involved in more automobile accidents than high school girls?” After conducting a hypothesis test, you conclude that there is sufficient evidence to reject the null hypothesis at α = 0.05. Use complete sentences to answer the following.

1. What were your null and alternative hypotheses in words?
   
2. State your conclusion pertaining to real-life in words.
   
3. If this conclusion is actually NOT correct, what type of error is this? State the correct conclusion in words.
   
4. What are some possible consequences of this error?
   
5. How might you change the alpha level to reduce this type of error? Explain.

Small-business telephone users were surveyed 6 months after access to carriers other than Carrier A became available for​ wide-area telephone service. Of a random sample of

260260

Carrier A​ users,

158158

said they were attempting to learn more about their​ options, as did

206206

of an independent random sample of

240240

users of alternate carriers.​ Test, at the

11​%

significance level against a​ two-sided alternative, the null hypothesis that the two population proportions are the same.

Let

Upper P Subscript xPx

be the proportion of Carrier A users who said they were attempting to learn more about their options and

Upper P Subscript yPy

be the proportion of users of alternate carriers who said they were attempting to learn more about their options.

H1=?

H0=?

The test statistic is Z=?

The critical​ value(s) is(are)=?

Since the test statistic is NOT MORE EXTREME/MORE EXTREME=?

than the critical​ value(s) DO NOT REJECT/REJECT=?

Upper H 0H0.

There is SUFFİCİENT/UNSUFFİCİENT=?evidence to conclude that there is a difference between the two population proportions.

In 2016, the global average annual income worldwide was estimated to be $10,850[1]. (This includes all countries of the world, not just the countries in the data table.)

[1] Source: Organization for Economic Co-operation and Development (OECD).

A) construct an 80%, 90%, 95%, 98%, 99% confidence interval to estimate the proportion of countries in the world with an average income greater than the global average. Calculate the Margin of Error for each confidence interval.

B) As the confidence level increases, what happens to the width of the interval? (Note: the width of the interval is the difference between the upper and lower limits.)

C) As the confidence level increases, what happens to the margin of error?

Suppose you have to pay $2 for a ticket to enter a competition. The prize is $18 and the probability that you win is 1/3. Your current wealth is $10.

(a) Are you going to enter this competition? Justify your decision, that is, choose a utility function that best describes your attitude toward, compute your expected utilities from entering the competition or staying away from it, and compare them to justify your decision.

1. Find a 95% confidence interval for the mean amount of money per capita spent on healthcare. (To do this you will need to use the variable health $ per capita in the Global Health Summary data set.) Round your answer to the nearest cent.
2. Describe what requirements must be met for this interval to be valid and whether you think that this data set meets these requirements.
3. Using a complete sentence, interpret the meaning of the confidence interval using the context of the problem.

***PLEASE SHOW HOW TO SOLVE IN EXCEL***

Case Problem 3:        Consumer Research, Inc.

(Copy the worksheet named “Consumer” in QMB3200-Homework#10Data.xlsx into your file for this problem)

Consumer Research, Inc., is an independent agency that conducts research on consumer attitudes and behaviors for a variety of firms. In one study, a client asked for an investigation of consumer characteristics that can be used to predict the amount charged by credit card users. Data were collected on annual income, household size, and annual credit card charges for a sample of 50 consumers and are provided in the worksheet named “Consumer.”

Managerial Report

1. Use methods of descriptive statistics to summarize the data. Comment on the findings.
2. Develop estimated regression equations, first using annual income as the independent variable and then using household size as the independent variable. Which variable is the better predictor of annual credit card charges? Discuss your findings.
3. Develop an estimated regression equation with annual income and household size as the independent variables. Discuss your findings.
4. What is the predicted annual credit card charge for a three-person household with an annual income of $40,000?
5. Discuss the need for other independent variables that could be added to the model. What additional variables might be helpful?

1. Marine biologists have noticed that the color of the outermost growth band on a clam tends to be related to the time of the year in which the clam dies. A biologist conducted a small investigation of whether this is true for the species Protothaca staminea. She collected a sample of 78 clam shells from the species and classified them according to the month when the clam died and the color of the outermost growth band. The data are provided below:

Color

Clear Dark Unreadable

February 9 25 7

March 15 18 4

Is there a significant difference in the color distribution between clams that died in February and March? Show your work and include all steps for full credit. Make sure all assumptions are met. (4pts)

2. The Wisconsin Fast Plant (Brassica campestris) has a very rapid growth cycle that makes it particularly well-suited for studying factors that affect plant growth. A random sample of plants was treated with the substance Ancymidol and compared a control group of plants that was given ordinary water. The heights of all of the plants were measured (in cm) after two weeks of growth:

Ancymidol 7.7, 12.8, 5.5, 19.0, 13.1, 8.2, 14.3

Control 19.2, 14.3, 21.2, 9.2, 20.4, 19.7

Conduct the appropriate test to determine if there is a difference in plant height after two weeks of growth if plants were given Ancymidol compared to water. Include all steps for full credit. (4pts)

An individual wanted to determine the relation that might exist between speed and miles per gallon of an automobile. Let X be the average speed of a car on the highway measured in miles per hour and let Y represent the miles per gallon of the automobile. The following data is collected:
X
50
55
55
60
60
62
65
65
Y
28
26
25
22
20
20
17
15
   •   In the space below, use technology to construct a scatterplot of the bivariate data set.




   •   What is the value for r? Interpret this value, would you say that the correlation is positive or negative? Strong or Weak? How do you know?



   •   From the regression equation given above, what value is the slope of the line? Interpret this slope, what does it tell us about the relationship between average speed and miles per gallon?

   •   Predict the miles per gallon of a car traveling 63 miles per hour.

   •   Predict the average speed of a car whose fuel mileage is 23 miles per gallon.


(f) Find r squared. What does this statistic tell us about between average speed and miles per gallon?


1. Elevated levels of plasma HDL cholesterol may be associated with lowered risk of coronary heart disease. Several studies have suggested that vigorous exercise may result in increased levels of HDL cholesterol. To investigate this theory, researchers measured HDL concentrations (mg/dL) in middle-aged (35-66 years) marathon runners, as well as inactive men. The data are summarized below. (Assume equal population variances in the two groups.)

sample size mean st. dev

Inactive men 70 43.3 14.2

Marathon runners 70 52.8 14.3

a. (4pts) Conduct a hypothesis test to see if marathon runners have significantly lower mean HDL cholesterol levels in this age group. Use α=0.05. Write your hypotheses, calculate the test statistic, and p-value, and write your conclusion. (SE = 2.41)

b. (2pts) Calculate the 90% confidence interval for the difference in mean HDL cholesterol among inactive men and marathon runners in this age group. Interpret your interval.

c. (1pt) State two ways in which the confidence interval in (i) could be made narrower.

d. (1pt) Use your interval in (b), Explain how this confidence interval corresponds to the results you found in part (a).

2. As part of a study of environmental influences on sex determination in the fish Menidia, eggs from a single mating were divided into two groups and raised in either a warm or a cold environment. The data show that 65 of 141 offspring in the warm environment and 107 of 169 offspring in the cold environment were females.

a. Test the hypothesis that the distribution of female and male fish follows a 1:1 ratio in the cold environment. Ascertain that your assumptions are met, and then do the test. (2pts)

b. What are the odds of the fish in the cold environment being female? (1pt)

c. Calculate the odds ratio of the fish being female in the cold environment compared to the warm environment. Interpret this odds ratio in the context of the question. (1pt)