apply statistical methods and analysis. Unless otherwise stated, use 5% (.05) as your alpha level (cutoff for statistical significance).


#1.  For each example, state whether the one-sample, two-independent-sample, or related-samples t test is most appropriate. If it is a related-samples t test, indicate whether the test is a repeated-measures design or a matched-pairs design.     

A professor tests whether students sitting in the front row score higher on an exam than students sitting in the back row.

A graduate student selects a sample of 25 participants to test whether the average time students attend to a task is greater than 30 minutes.

A researcher matches right-handed and left-handed siblings to test whether right-handed siblings express greater emotional intelligence than left-handed siblings.

A principal at a local school wants to know how much students gain from being in an honors class. He gives students in an honors English class a test prior to the school year and again at the end of the school year to measure how much students learned during the year.

#2.

A random sample of 25 professional basketball players shows a mean height of 6 feet, 5 inches with a 95% confidence interval of 0.4 inches. Explain what this indicates.

If the sample were smaller, would the confidence interval become smaller or larger? Explain.

If you wanted a higher level of confidence (99%) would the confidence interval become smaller or larger? Explain.

These weekly exercises provide the opportunity for you to understand and apply statistical methods and analysis. Unless otherwise stated, use 5% (.05) as your alpha level (cutoff for statistical significance). #

1. Which type of ANOVA would you use for each of the studies below? • One-way between subjects (independent groups) • One-way within subjects (repeated measures) • Two-way between subjects

a. Measure the self-esteem of the same group of college students at the beginning, middle and end of their freshman year.

b. Compare math skills for three different professional groups: physicians, attorneys and psychologists.

c. Measure Body Mass Index (BMI) for persons who take Supplement X vs. a placebo and who either exercise regularly or don’t. So there are four groups: 1) Exercise/Take Supplement X, 2) Don’t Exercise/Take Supplement X, 3) Exercise/Take Placebo, 4) Don’t Exercise/Take Placebo

d. Look at satisfaction with mental health services based on the client’s ethnicity (White, Black, Hispanic, Asian or Other) and how they were greeted on their initial visit (receptionist smiles or does not smile).

apply statistical methods and analysis. Unless otherwise stated, use 5% (.05) as your alpha level (cutoff for statistical significance).

The chi-square statistic is 5.143. The p-value is .0233. This result is significant at p < .05.
#1. The chart above shows male and female preferences for vanilla vs. chocolate ice cream among men and women.

1. What percent of men prefer chocolate over vanilla? ________
2. What percent of women prefer chocolate over vanilla? ________
3. Report the results of the statistical test in plain language:

#2. The calculator at this link will allow you to perform a one-way chi-square or “goodness of fit test”:
http://vassarstats.net/csfit.html

Fifty students can choose between four different professors to take Introductory Statistics. The number choosing each professor is shown below. Use the calculator above to test the null hypothesis that there is no preference for professors -- that there is an equal chance of choosing each of them. Report your results including chi-square, degrees of freedom, p-value and your interpretation. Use an alpha level of .05. Be careful not to over interpret – state only what the test result tells you.

#3. Match these non-parametric statistical tests with their parametric counterpart by putting the corresponding letter on the line.
_____ Friedman test
_____ Kruskal-Wallis H test
_____ Mann-Whitney U test
_____ Wilcoxon Signed-Ranks T test

A: Paired-sample t-test
B: Independent-sample t-test
C: One-way ANOVA, independent samples
D: One-way ANOVA, repeated measures

1. According to a 2011 report by the U.S. Department of Labor, civilian Americans spend 2.75 hours per day watching television. A faculty researcher, Dr. Sameer, at California Polytechnic State University (Cal Poly) conducts a study to see whether a different average applies to Cal Poly students. He surveys a random sample of 100 Cal Poly students and finds the mean number of hours spent watching TV is 3.07 hours. The sample standard deviation is 1 hour. The sample distribution is not strongly skewed.

a. Describe the parameter in words. Assign a symbol to it.

b. What is the value for the statistic? Assign a symbol to it.

c. Describe the null hypothesis in words.

d. Describe the alternative hypothesis in words.

e. Write your null hypothesis and alternative hypothesis from part c and d using symbols.

f. Why we can use theory-based approach for this study?

g. Calculate the t-statistic. Show your work. h. Based on your t-statistic, do you have strong evidence against the null hypothesis?

i. Based on your result from part h, what type of error may occur?

j. Describe the type of error you identify in part I in the context of the question.

Dana Rand owns a catering company that prepares banquets and parties for both individual and business functions throughout the year. Rand’s business is seasonal, with a heavy schedule during the summer months and the year-end holidays and a light schedule at other times. During peak periods, there are extra costs; however, even during nonpeak periods Rand must work more to cover her expenses.

One of the major events Rand’s customers request is a cocktail party. She offers a standard cocktail party and has developed the following cost structure on a per-person basis.

When bidding on cocktail parties, Rand adds a 15 percent markup to this cost structure as a profit margin. Rand is quite certain about her estimates of the prime costs but is not as comfortable with the overhead estimate. This estimate was based on the actual data for the past 12 months presented in the following table. These data indicate that overhead expenses vary with the direct-labor hours expended. The $13 estimate was determined by dividing total overhead expended for the 12 months ($782,000) by total labor hours (58,500) and rounding to the nearest dollar.

Rand recently attended a meeting of the local chamber of commerce and heard a business consultant discuss regression analysis and its business applications. After the meeting, Rand decided to do a regression analysis of the overhead data she had collected. The following results were obtained.

Required:

2. Using data from the regression analysis, develop the following cost estimates per person for a cocktail party. Assume that the level of activity remains within the relevant range. a. variable cost per person? b. absorption (full) cost per person?

3. Dana Rand has been asked to prepare a bid for a 240-person cocktail party to be given next month. Determine the minimum bid price that Rand should be willing to submit. Minimum Bid Price?

4. What other factors should Dana Rand consider in developing the bid price for the cocktail party?

The chart below shows the correct answers for 4. in order.

If data set A has a larger standard deviation than data set B, what would be different about their distributions?

What is the value to us in the twenty-first century of having an accurate demographic picture of earlier centuries? Explain in detail and provide an example.

Choose the most appropriate statistic for measuring spread for the following data sets.

a.) A medical survey asks for patients' body fat percentages. Most people in the study had body fat percentages in the 20's, while a few had body fat percentages over 40. Which is the best measure of the spread of body fat percentages?

range, proportion, standard deviation, IQR, median, or mean

b.) The same survey also asks for patients' heights. Which is the best measure of the spread of height?

range, proportion, standard deviation, IQR, median, or mean

2. To see why this is relevant to our analysis of the arrangement of energy in degrees of freedom, first take a simple problem in the ways that you can arrange some cards from a deck.

a. Suppose you have only the numbered cards from one suit (say hearts) of one deck (numbered from Ace = 1 to 10). If you choose 4 of those cards at random, how many different sets of those cards could you get? (Order doesn't matter, so 10-9-8-7 is considered the same as 7-8-9-10.)

b. If you now select from the numbered cards from a different suit (say spades) of that deck and choose 3 of those cards at random, how many different sets of the spades could you get?

c. If you select BOTH four hearts and three spades at random, how many different sets of cards could you get?

Question 7

The following lists of data represent five separate departments' technicians overtime for a week. Which has the smallest standard deviation?

Select the correct answer below:

a)28, 26, 20, 17, 21, 29, 28, 28, 17, 22

b)14, 15, 15, 12, 11, 14, 11, 13, 14, 12

c)34, 26, 34, 26, 22, 34, 24, 26, 25, 24

d)21, 15, 14, 27, 21, 24, 27, 20, 20, 30

e)9, 17, 21, 9, 14, 18, 22, 10, 12, 16

Question 8

A deck of cards contains RED cards numbered 1,2,3,4,5,6 and BLUE cards numbered 1,2,3. Let R be the event of drawing a red card, B the event of drawing a blue card, E the event of drawing an even numbered card, and O the event of drawing an odd card.

Drawing the Blue 2 is an example of which of the following events? Select all correct answers.

Select all that apply:

B AND O

R OR E

E′

B′

R AND E

O′

B AND E

Question 9

If A and B are events with P(A)=0.2, P(A OR B)=0.62, and P(A AND B)=0.18, find P(B).

Provide your answer below:

Question 10

The probability of buying a movie ticket with a popcorn coupon is 0.608. If you buy 10 movie tickets, what is the probability that 3 or more of the tickets have popcorn coupons? (Round your answer to 3 decimal places if necessary.)

Provide your answer below:

P(X greater than or equal to 3)=

Question 11

At a certain company, the mentoring program and the community outreach program meet at the same time, so it is impossible for an employee to do both. If the probability that an employee participates in the mentoring program is 0.51, and the probability that an employee participates in the outreach program is 0.21, what is the probability that an employee does the mentoring program or the community outreach program?

Provide your answer below:

Question 12

A grain elevator measures the weight of each truck that delivers grain to their site. What is the level of measurement of the data?

a)Nominal

b)Ordinal

c)Interval

d)Ratio

Question 13

Let W be the event that a randomly chosen person works for the city government. Let V be the event that a randomly chosen person will vote in the election. Place the correct event in each response box below to show:

Given that the person works for the city government, the probability that a randomly chosen person has will vote in the election.

P(_ _ )

Question 14

Carlos and Devon both accepted new jobs at different companies. Carlos's starting salary is $42,000 and Devon's starting salary is $40,000. They are curious to know who has the better starting salary, when compared to the salary distributions of their new employers.

A website that collects salary information from a sample of employees for a number of major employers reports that Carlos's company offers a mean salary of $52,000 with a standard deviation of $8,000. Devon's company offers a mean salary of $48,000 with a standard deviation of $5,000.

Find the z-scores corresponding to each of their starting salaries. Round to two decimal places, if necessary.

Provide your answer below:

Carlos's z-score:

Devon's z-score:

Question 15

A deck of cards contains RED cards numbered 1,2,3,4,5, BLUE cards numbered 1,2,3,4,5,6, and GREEN cards numbered 1,2. If a single card is picked at random, what is the probability that the card is GREEN?

Select the correct answer below:

6/13

3/13

5/13

2/13

12/13

10/13

How do I do  independent t test on the data set below and how do I know if its pooled t test or unrolled t test?

Health question for reference: to what extend does the age of MI patients vary by gender

Standard deviation: male = 13.944 female= 13.939

mean: male 65.353 female=73.628

Male female

65   88
77   81
78   82
76   66
40   81
83   73
58   64
43   53
39   69
66   67
61   89
49   85
85   81
54   85
82   84
68   83
78   76
56   77
72   84
50   43
75   87
61   70
48   64
82   59
62   91
39   60
45   80
65   72
68   73
73   85
64   80
80   79
74   48
80   32
92   86
51
41
90
83
61
64   
82
48
63
81
52   
65   
74
62
71
73
43
80
72
57
76
53
44
71
64
86
60
63
74
56

7. A certain sports car model has a 0.07 probability of defective steering and a 0.11 probability of defective brakes. Erich S -E just purchased one of the models. If the two problems are statistically independent, determine the probability

a. Erich’s car has both defective steering and defective brakes.

b. Erich’s car has neither defective steering nor defective brakes.

c. Erich’s car has either defective steering only or defective brakes only (meaning exactly one of the two, but not both, defects).

5. Arsalaan A., a well-known financial analyst, selected 50 consecutive years of U.S. financial markets data at random. For 11 of the years, the rate of return for the Dow Jones Industrial Average [DJIA] exceeded the rates of return for both the S&P 500 Index and the NASDAQ Composite Index. For 8 of the years, the rate of return for the DJIA trailed the rates of return for both the S&P 500 and the NASDAQ. For 21 of the years, the rate of return for the DJIA trailed the rate of return for the S&P 500. Over the 50 years,

a. determine the probability the rate of return for the DJIA trailed the rate of return for the NASDAQ.

b. determine the probability the rate of return for the DJIA trailed the rate of return for at least one of the other two Indexes.

c. determine the probability the rate of return for the DJIA trailed the rate of return for the S&P 500 given it trailed the rate of return for the NASDAQ.

d. determine the probability the rate of return for the DJIA exceeded the rate of return for the S&P 500 given it exceeded the rate of return for the NASDAQ.

Let X have a binomial distribution with parameters

n = 25

and p. Calculate each of the following probabilities using the normal approximation (with the continuity correction) for the cases

p = 0.5, 0.6, and 0.8

and compare to the exact binomial probabilities calculated directly from the formula for

b(x; n, p).

(Round your answers to four decimal places.)

(a)

P(15 ≤ X ≤ 20)

(b)

P(X ≤ 15)

(c)

P(20 ≤ X)

Let Z be a standard normal random variable and calculate the following probabilities, drawing pictures wherever appropriate. (Round your answers to four decimal places.) (a) P(0 ≤ Z ≤ 2.13) (b) P(0 ≤ Z ≤ 1) (c) P(−2.20 ≤ Z ≤ 0) (d) P(−2.20 ≤ Z ≤ 2.20) (e) P(Z ≤ 1.93) (f) P(−1.15 ≤ Z) (g) P(−1.20 ≤ Z ≤ 2.00) (h) P(1.93 ≤ Z ≤ 2.50) (i) P(1.20 ≤ Z) (j) P(|Z| ≤ 2.50)