An air transport association surveys business travelers to develop quality ratings for transatlantic gateway airports. The maximum possible rating is 10. Suppose a simple random sample of 50 business travelers is selected and each traveler is asked to provide a rating for a certain airport. The ratings obtained from the sample of 50 business travelers follow.

Develop a 95% confidence interval estimate of the population mean rating for this airport. (Round your answers to two decimal places.)

? to ?

For these discussion questions:

Define Type I and Type II error and explain their importance in statistical research (5 points).

Discuss the use of directional and non-directional hypotheses. How do we make the decision to use directional or non-directional tests? (5 points)

For a standard normal curve, find the z scores for the following: the lower and upper z-scores for the middle .7994

The average score for male golfers is 87 and the average score for female golfers is 102. Use these values as the population means for men and women and assume that the population standard deviation σ = 14 strokes for both. A simple random sample of 32 male golfers and another simple random sample of 36 female golfers will be taken.

a. Calculate the standard error of the mean for both male and female golfers.

b. What is the probability that the sample mean is within 3 strokes of the populations mean for the sample of male golfers?

c. What is the probability that the sample mean is within 3 strokes of the populations mean for the sample of female golfers?

d. In which case, part (b) or part (c), is the probability of obtaining a sample mean within 3 strokes of the population mean higher? Why?

1. When faced with a problem or choice, humans can use two different strategies: "cognitive reflectivity," which results in slower responses and few mistakes, or "cognitive impulsivity," which results in quicker responses but also more mistakes. Depending on the individual, these two strategies are used differently. A pilot experiment was conducted on 22 right-handed individuals who were administered a cognitive reflectivity-impulsivity questionnaire, while recording voxel-based morphometry (regional gray matter density) in the ventral medial prefrontal cortex.

   Based on the experimental design and the kind of data collected, which statistical test(s) should be used to determine whether there is an association between the cognitive strategy, cognitive reflectivity and the gray matter density of the ventral medial prefrontal cortex? SELECT ALL THAT APPLY!

   		two sample t-test
   		z-test
   		One-way ANOVA
   		correlation coefficient (r)
   		t-test of zero linear correlation

A doctor would like to evaluate whether flu-frequency is different among patients of various ages. He groups his most recent 12 patients into four groups according to age (pediatric, young adult, older adult, senior), and counts the frequency of their flu-related visits. Below is his data. Test the hypothesis that flu frequency is different among pediatric, adult, older adult, and senior patients using an alpha level of .01.

  Find the critical value:

  Calculate the obtained statistic:

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

(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:

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)

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.

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?

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?

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.

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