12.1 Determine the Pearson product-moment correlation coefficient for the following data.

x	1	11	9	7	5	3	2
y	9	4	6	5	7	7	8

(Do not round the intermediate values. Round your answer to 3 decimal places.)


Correlation coefficient, r = enter the Correlation coefficient rounded to 3 decimal places

The HeadStart runs a day camp for 6- to 10- year olds during the summer. Its manager is trying to reduce the center's operating costs to avoid having to raise the tuition fee. The manager is currently planning what to feed the children for lunch. She would like to keep costs to a minimum, but also wants to make sure she is meeting the nutritional requirements of the children. She has already decided to go with peanut butter and jelly sandwiches, and some combination of apples, milk, and/or cranberry juice. The nutritional content of each food choice and its cost are given in the table below:

	Bread	Peanut Butter	Jelly		Milk	Juice
	(slice)	(tbsp)	(tbsp)	Apples	(cup)	(cup)
Unit Cost	$0.06	$0.05	$0.08	$0.35	$0.20	$0.40
			Nutritional Data
Calories from Fat	15	80	0	0	60	0
Calories	80	100	70	90	120	110
Vitamin C (mg)	0	0	4	6	2	80
Fiber (g)	4	0	3	10	0	1

The nutritional requirements are as follow. Each child should receive between 300 and 500 calories, but no more than 30% of these calories should come from fat. Each child should receive at least 60 milligrams (mg) of vitamin C and at least 10 grams (g) of fiber.

To ensure tasty sandwiches, the manager wants each child to have a minimum of 2 slices of bread, 1 tablespoon (tbsp) of peanut butter, and 1 tbsp of jelly, along with at least 1 cup of liquid (milk and/or cranberry juice).

The manager would like to select the food choices that would minimize cost while meeting all these requirements.

Formulate and solve a linear programming model for this problem on a spreadsheet.

a) How many ounces of each type of food are included in one serving of the lunch? (Round to three decimals)

	Bread	Peanut Butter	Jelly	Apples	Milk	Juice
	(slice)	(tbsp)	(tbsp)		(cup)	(cup)
Diet (ounces)

b) How many calories from fat are in one serving of the lunch? (Round to three decimals)

c) What is the total cost per serving of the lunch? (Round to two decimals) $

Below is a list of gas mileage ratings for selected passenger cars in miles per gallon.

16.2 20.3 31.5 30.5 21.5 31.9 37.3 27.5 27.2 34.1 35.1 29.5 31.8 22.0 17.0 21.6

Find the mean, standard deviation, five - number summary, IQR, and identify any outliers. Use the five - number summary to sketch a boxplot. What does the boxplot tell you about the distribution of the data? (20 points)

Some Alzheimer’s caregivers were asked to respond to the following statement: “Caregiving enabled me to develop a more positive attitude toward life.” The responses are reflected in the following table.

Strongly Disagree	Somewhat Disagree	No Opinion	Somewhat Agree	Strongly Agree
166	116	171	234	542

1. Graph the data. Based on your graph, is there evidence to suggest the distribution is not uniform?
2. Run a statistical test to see if the data indicate the true distribution is not uniform. State the hypotheses, obtain a p-value, and state your conclusion.

In preparing for the upcoming holiday season, Fresh Toy Company (FTC) designed a new doll called The Dougie that teaches children how to dance. The fixed cost to produce the doll is $100,000. The variable cost, which includes material, labor, and shipping costs, is $34 per doll. During the holiday selling season, FTC will sell the dolls for $42 each. If FTC overproduces the dolls, the excess dolls will be sold in January through a distributor who has agreed to pay FTC $10 per doll. Demand for new toys during the holiday selling season is extremely uncertain. Forecasts are for expected sales of 60,000 dolls with a standard deviation of 15,000. The normal probability distribution is assumed to be a good description of the demand. FTC has tentatively decided to produce 60,000 units (the same as average demand), but it wants to conduct an analysis regarding this production quantity before finalizing the decision.

a. Create a what-if spreadsheet model using a formula that relate the values of production quantity, demand, sales, revenue from sales, amount of surplus, revenue from sales of surplus, total cost, and net profit. What is the profit corresponding to average demand (60,000 units)?

$

b.Modeling demand as a normal random variable with a mean of 60,000 and a standard deviation of 15,000, simulate the sales of the Dougie doll using a production quantity of 60,000 units. What is the estimate of the average profit associated with the production quantity of 60,000 dolls? Round your answer to the nearest dollar.

$

c.Before making a final decision on the production quantity, management wants an analysis of a more aggressive 70,000-unit production quantity and a more conservative 50,000-unit production quantity. Run your simulation with these two production quantities. What is the mean profit associated with each? Round your answers to the nearest dollar.

50,000- unit production quantity: $

70,000- unit production quantity: $

d.Compare the three production quantities (50,000, 60,000, and 70,000) using all these factors. What trade-off occurs for the probability that a shortage occurs? Round your answers to 3 decimal places.

50,000 units :

60,000 units :

70,000 units :

According to the WHO MONICA Project the mean blood pressure for people in China is 128 mmHg with a standard deviation of 23 mmHg (Kuulasmaa, Hense&Tolonen, 1998). Blood pressure is normally distributed.

A.State the random variable.

B. Suppose a sample of size 15 is taken. State the shape of the distribution of the sample mean.

C. Suppose a sample of size 15 is taken. State the mean of the sample mean.

D.Suppose a sample of size 15 is taken. State the standard deviation of the sample mean.

E. Suppose a sample of size 15 is taken. Find the probability that the sample mean blood pressure is more than 135 mmHg.

F. Would it be unusual to find a sample mean of 15 people in China of more than 135 mmHg? Why or why not?

If you did find a sample mean for 15 people in China to be more than 135 mmHg, what might you conclude?

Nonparametric tests should not be used when ______.

the associations being tested involve categorical variables

the dependent variables are ordinal scales

the assumptions of parametric tests are met

the population distribution is heavily skewed

The chi-square tests are used to analyze ______.

Medians

frequency of data

continuous variables

skewness

The ______ tests are more powerful than the ______ tests, which means the ______ is higher for nonparametric tests.

parametric; nonparametric; type II error

nonparametric; parametric; type I error

parametric; nonparametric; type I error

nonparametric; parametric; type II error

If a 3 × 3 table is presented, then you know that a study used ______ independent variables each with ______ categories.

nine; two

two; four

three; three

two; three

Expected frequencies are obtained in rows-by-columns table assuming that the row and column categorizations are ______.

independent of each other

equal

related to each other

dependent on each other

Which of the following is a possible null hypothesis for a chi-square test?

The two categorical variables are unrelated in the population.

The means of populations in two independent groups are equal.

The two categorical variables are related in the population.

The distribution of scores for the first population is different from the distribution of scores for the second population.

If you have a 5 × 5 frequency table, then the critical value of chi-square would be based on ______ degrees of freedom.

16

8

10

25

Below are the number of acts of graffiti that occur on walls painted white, painted blue, or covered with chalkboard. H_o is frequencies of graffiti are equal in the population. With N = 30, f_e = N/k = 30/3 = 10 for each category.

What is the critical value for this test?

White	Blue	Chalk
fo = 8	fo = 8	fo = 8
fe = 10	fe = 10	fe = 10

3.84

5.99

9.21

9.57

Below are the number of acts of graffiti that occur on walls painted white, painted blue, or covered with chalkboard. H_o is frequencies of graffiti are equal in the population. With N = 30, f_e = N/k = 30/3 = 10 for each category.

What is the appropriate obtained value for this test?

White	Blue	Chalk
fo = 8	fo = 8	fo = 8
fe = 10	fe = 10	fe = 10

7.80

2.60

3.90

5.99

Below are the number of acts of graffiti that occur on walls painted white, painted blue, or covered with chalkboard. H_o is frequencies of graffiti are equal in the population. With N = 30, f_e = N/k = 30/3 = 10 for each category.

In the population, we expect _____% of graffiti on white walls, _____% on blue walls, and _____% on chalkboard walls.

White	Blue	Chalk
fo = 8	fo = 8	fo = 8
fe = 10	fe = 10	fe = 10

58%; 21%; 19%

27%; 17%; 57%

50%; 25%; 25%

33%; 33%; 33%

A company that manufactures electronic components wants to know the mean discharge time of one particular type of capacitor that it makes. In order to estimate this value, they randomly select 100 capacitors and measure how long they take to discharge. The mean of this sample was 7.25 seconds with a standard deviation of 0.15 seconds. Assuming that this distribution is normal, construct a 99% confidence interval to estimate the mean discharge time for all capacitors of this type. Since this is a Confidence Interval for a mean, what distribution would be used to calculate the critical value? Standard Normal Distribution t-Distribution Binomial Distribution You get to choose the distribution you prefer

A stationery store wants to estimate the mean retail value of greeting cards that it has in its inventory. A random sample of 100 greeting cards indicates a mean value of ​$2.53 and a standard deviation of ​$0.41 . Complete parts​ (a) and​ (b).

A. Is there evidence that the population mean retail value of the greeting cards is different from $2.50 ​? ​(Use a 0.10 level of​ significance.)

State the null and alternative hypothesis. Identify the critical value(s). Determine the test statistic. What is the conclusion?

B. Determine the p-value and interpret its meaning

Plastic Microfiber Pollution on Shorelines

In a study, we see that plastic microparticles are contaminating the world’s shorelines and that much of the pollution appears to come from fibers from washing polyester clothes. The same study also took samples from ocean beaches. Five samples were taken from each of 18 different shorelines worldwide, for a total of 90 samples of size 250 mL. The mean number of plastic microparticles found per 250 mL of sediment was 18.3 with a standard deviation of 8.2 .

(a) Find a 90% confidence interval for the mean number of polyester microfibers per 250 mL of beach sediment.

Round your answers to two decimal places.

The 90% confidence interval is

(b) What is the margin of error?

Round your answer to two decimal places.

margin of error =

(C) If we want a margin of error of only ±1 with 90% confidence, what sample size is needed?

Round your answer up to the nearest integer.

sample size =

A used car dealer says that the mean price of a​ three-year-old sports utility vehicle is ​$ 22 comma 000 22,000. You suspect this claim is incorrect and find that a random sample of 22 22 similar vehicles has a mean price of ​$ 22 comma 668 22,668 and a standard deviation of ​$ 1919 1919. Is there enough evidence to reject the claim at alpha α equals = 0.05 0.05​? Complete parts​ (a) through​ (e) below. Assume the population is normally distributed. ​(a) Write the claim mathematically and identify Upper H 0 H0 and Upper H Subscript a Ha. Which of the following correctly states Upper H 0 H0 and Upper H Subscript a Ha​? A. Upper H 0 H0​: mu μ equals =​$ 22 comma 000 22,000 Upper H Subscript a Ha​: mu μ less than <​$ 22 comma 000 22,000 B. Upper H 0 H0​: mu μ greater than or equals ≥​$ 22 comma 000 22,000 Upper H Subscript a Ha​: mu μ less than <​$ 22 comma 000 22,000 C. Upper H 0 H0​: mu μ equals =​$ 22 comma 000 22,000 Upper H Subscript a Ha​: mu μ greater than >​$ 22 comma 000 22,000 D. Upper H 0 H0​: mu μ not equals ≠​$ 22 comma 000 22,000 Upper H Subscript a Ha​: mu μ equals =​$ 22 comma 000 22,000 E. Upper H 0 H0​: mu μ equals =​$ 22 comma 000 22,000 Upper H Subscript a Ha​: mu μ not equals ≠​$ 22 comma 000 22,000 F. Upper H 0 H0​: mu μ greater than >​$ 22 comma 000 22,000 Upper H Subscript a Ha​: mu μ less than or equals ≤​$ 22 comma 000 22,000 ​(b) Find the critical​ value(s) and identify the rejection​ region(s). What​ is(are) the critical​ value(s), t 0 t0​? t 0 t0 equals = nothing ​(Use a comma to separate answers as needed. Round to three decimal places as​ needed.) Determine the rejection​ region(s). Select the correct choice below and fill in the answer​ box(es) within your choice. ​(Round to three decimal places as​ needed.) A. nothing less than nothing C. t less than < nothing D. t less than < nothing and t greater than > nothing ​(c) Find the standardized test statistic t. t equals = nothing ​(Round to two decimal places as​ needed.) ​(d) Decide whether to reject or fail to reject the null hypothesis.

A researcher conducts an experiment to compare the effectiveness of different therapies for depression. Participants diagnosed with depression are randomly assigned to one of four groups: Control (no therapy provided), antidepressant medication (SSRI), cognitive-behavioral therapy (CBT), or a combination of medication and cognitive-behavioral therapy (SSRI+CBT). The DV is depression severity after 4 weeks, with higher scores indicating the presence of more depressive symptoms.

SSRI	CBT	SSRI+CBT	Control
11	7	9	12
5	9	6	7
9	6	7	11
7	11	9	9
6	7	5	6
9	6	8	8
11	9	6	11
10	8	4	10
8	7	8	12
9	9	9	9

Is there a statistically significant difference between the groups? With α = .05, perform a oneway between groups ANOVA to find out.

a. Perform the ANOVA in Excel by creating your own formulas and with the FDIST function to determine p. Create your own full summary table.

b. Compute the effect size (eta squared).

c. Create either a bar graph comparing the means of the four groups (including standard error bars) or a box-plot display comparing the four groups.

d. Insert a textbox reporting your statistical and research conclusion.

A system is composed of five components, each of which is either working or failed. Consider an experiment that consists of observing the status of each component, and let the outcome of the experiment be given by the vector (x1, x2, x3, x4, x5) where xi is equal to 1 if component i is working and is equal to 0 if component i has failed. Suppose that two components are working and three components have failed. In how many ways can this occur?

Although union and non union wages tend to rise at the same rate in the long run, union wages usually advance faster during recessions and early in period of recovery, and non union wages tend to advance more rapidly later in the business cycle when the labor markets are tight. To examine this issue, an economist records the hourly wages (including employee benefits) of employees with two years experience for twelve chosen consumer products manufacturing firms. Six non union shops and six consumer manufacturing firms with union shops. The data (in dollars) are as follows:

Non union shops: 8.26, 8.17, 8.45, 9.09, 8.85, 8.31

Union shops: 7.92, 8.39, 8.64, 8.04, 8.24, 8.25

A) At 5% level of significance, does the data suggest that the union and non-union wages differ, on the average, for employees with two years experience in the consumer products manufacturing industry? Show all necessary work.

B) What type of error is possible and describe this error in terms of the problem?

C) Estimate the difference between the actual average wages of union and non-union employees with two years experience in the consumer products manufacturing industry using a 90% confidence interval. Does the data suggest that there is sufficient evidence of a difference in the actual average wage of union and non-union employees with 2 years experience in the consumer products manufacturing industry? Show all necessary work.

D) Interpret the interval estimation.

The dataset gives the dried weight in pounds of three groups of 10 batches of plants, where each group of 10 batches received a different treatment. The Weight variable gives the weight of the batch and the Groups variable gives the treatment received.

A.) Conduct an analysis of variance to test the hypothesis of no difference in the weights of the plants under different treatments.

B.) Plot and analyze the residuals from the study and comment on model adequacy (All tests are to be performed at α = 0.05)

Control	Group 1	Group 2
4.17	4.81	6.31
5.58	4.17	5.12
5.18	4.41	5.54
6.11	3.59	5.5
4.5	5.87	5.37
4.61	3.83	5.29
5.17	6.03	4.92
4.53	4.89	6.15
5.33	4.32	5.8
5.14	4.69	5.26