Listed below are attractiveness ratings made by participants in a speed dating session. Each attribute rating is the sum of the ratings of five attributes (sincerity, intelligence, fun, ambition, shared interests).

Use a 0.05 significance level to test the claim that there is a difference between female attractiveness ratings and male attractiveness rating by following the steps below:

(a) State the null and alternative hypotheses, indicate the significance level and the type of test (left-, right-, or two-tailed test).

(b) Calculate by hand the test statistic.

(c) Use the appropriate sheet in the Hypothesis Test and Confidence Interval template to complete all relevant computations (including the test statistic: compare with (b) to confirm your calculation is correct).

(d) Use the P-value obtained in (c) to explain whether or not the null hypothesis is rejected.

(e) What can be concluded based off this data?

(f) Are there any potential issues related to the validation of the result (Hint: the subjective nature of the measures)

Instructions This assignment is to be typed up in the supplied R-Script. You need to show all of your work in R in the given script.

3. Infant mortality. The infant mortality rate is defined as the number of infant deaths per 1,000 live births. This rate is often used as an indicator of the level of health in a country. The relative frequency histogram below shows the distribution of estimated infant death rates for 224 countries for which such data were available in 2014.

(a) Estimate Q1, the median, and Q3 from the histogram.

(b) Would you expect the mean of this data set to be smaller or larger than the median? Explain your reasoning.

(c) If you calculated the z-score for the median in this distribution, would the result be positive or negative? Explain your reasoning.

The United States Golf Association tests golf balls to ensure that they conform to the rules of
golf. Balls are tested for weight, diameter, roundness and overall distance. The overall distance test is
conducted by hitting balls with a driver swung by a mechanical device nicknamed “Iron Byron” after the
legendary great Byron Nelson, whose swing the machine is said to emulate. Following are 100 distances
(in yards) achieved by a particular brand of golf ball in the overall distance test.

261.3 259.4 265.7 270.6 274.2 261.4 254.5 283.7 258.1 270.5
255.1 268.9 267.4 253.6 234.3 263.2 254.2 270.7 233.7 263.5
244.5 251.8 259.5 257.5 257.7 272.6 253.7 262.2 252.0 280.3
274.9 233.7 237.9 274.0 264.5 244.8 264.0 268.3 272.1 260.2
255.8 260.7 245.5 279.6 237.8 278.5 273.3 263.7 241.4 260.6
280.3 272.7 261.0 260.0 279.3 252.1 244.3 272.2 248.3 278.7
236.0 271.2 279.8 245.6 241.2 251.1 267.0 273.4 247.7 254.8
272.8 270.5 254.4 232.1 271.5 242.9 273.6 256.1 251.6 256.8
273.0 240.8 276.6 264.5 264.5 226.8 255.3 266.6 250.2 255.8
285.3 255.4 240.5 255.0 273.2 251.4 276.1 277.8 266.8 268.5

Construct a frequency distribution for these data using 13 bins. Draw the histogram

When an opinion poll calls landline telephone numbers at random, approximately 30% of the numbers are working residential phone numbers. The remainder are either non-residential, non-working, or computer/fax numbers. You watch the random dialing machine make 20 calls. (Round your answers to four decimal places.)

(a) What is the probability that exactly 4 calls reach working residential numbers?


(b) What is the probability that at most 4 calls reach working residential numbers?


(c) What is the probability that at least 4 calls reach working residential numbers?


(d) What is the probability that fewer than 4 calls reach working residential numbers?


(e) What is the probability that more than 4 calls reach working residential numbers?

A standardized exam consists of three parts: math, writing, and critical reading. Sample data showing the math and writing scores for a sample of 12 students who took the exam follow.

(a)

Use a 0.05 level of significance and test for a difference between the population mean for the math scores and the population mean for the writing scores. (Use math score − writing score.)

Formulate the hypotheses.

H₀: μ_d ≤ 0

H_a: μ_d = 0

H₀: μ_d ≠ 0

H_a: μ_d = 0

H₀: μ_d > 0

H_a: μ_d ≤ 0

H₀: μ_d = 0

H_a: μ_d ≠ 0

H₀: μ_d ≤ 0

H_a: μ_d > 0

Calculate the test statistic. (Round your answer to three decimal places.)

Calculate the p-value. (Round your answer to four decimal places.)

p-value =

What is your conclusion?

Do not reject H₀. We can conclude that there is a significant difference between the population mean scores for the math test and the writing test. Reject H₀. We can conclude that there is a significant difference between the population mean scores for the math test and the writing test.      Do not reject H₀. We cannot conclude that there is a significant difference between the population mean scores for the math test and the writing test. Reject H₀. We cannot conclude that there is a significant difference between the population mean scores for the math test and the writing test.

(b)

What is the point estimate of the difference between the mean scores for the two tests? (Use math score − writing score.)

What are the estimates of the population mean scores for the two tests?

Math:?

Writing:?

Which test reports the higher mean score?

The math test reports a / lower or higher /mean score than the writing test.

Determine the best way to model the relationship between the radon measurement A and B.

3a) graph with your best model represented on it.

3b) What told you it was the best model?

3c) Show your regression model for predicting radon B.

The chefs at a local pizza chain, strive to maintain the suggested size of their 16-inch pizzas. Despite their best efforts, they are unable to make every pizza exactly 16 inches in diameter. The manager has determined that the size of the pizzas is normally distributed with a mean of 16 inches and a standard deviation of 0.8 inch.

a. What are the expected value and the standard error of the sample mean derived from a random sample of 2 pizzas?

b. What are the expected value and the standard error of the sample mean derived from a random sample of 4 pizzas?

c. Compare the expected value and the standard error of the sample mean with those of an individual pizza.

If E(X) = 5, V(X) = 3 and Y = 5 - X/3 - X, what is mean of Y?

The table represents the answers of 80 respondents to the survey “How much sports
trainings do you have every year?” carried out among college students. Construct a stem-and-leaf
diagram for the data. Calculate the median and quartiles of these data.

129 157 154 191 192 142 188 126 128 180
190 166 157 147 155 154 200 128 167 143
131 156 153 168 149 144 155 188 149 142
160 149 184 187 169 161 157 134 122 173
188 183 178 148 135 188 187 166 121 177
169 182 158 169 146 173 133 189 183 143
148 121 181 145 189 120 122 189 146 190
128 142 189 131 199 182 197 148 157 140

The article “Determination of Carboxyhemoglobin Levels and Health Effects on Officers Working at the Istanbul Bosphorus Bridge” (G. Kocasoy and H. Yalin, Journal of Environmental Science and Health, 2004:1129–1139) presents assessments of health outcomes of people working in an environment with high levels of carbon monoxide (CO). Following are the numbers of workers reporting various symptoms, categorized by work shift. The numbers were read from a graph.

Can you conclude that the proportions of workers with the various symptoms differ among the shifts?

(a) State the appropriate null hypothesis.

(b) Compute the expected values under the null hypothesis.

(c) Compute the value of the chi-square statistic.

(d) Find the p-value. What do you conclude?

Suppose two Gaussian R.V.'s X and Y follow (X,Y)~N(1, 0; 1, 4, 0.5), and W=3X+Y. Find the joint PDF between W and Y, fwy(w,y) and find E{W|Y=y}.

What is the critical value of the correlation coefficient needed for rejection of the null hypothesis if your degrees of freedom is 30 and you are conducting a two-tailed test using the .05 level of significance?

The numbers racket is a well‑entrenched illegal gambling operation in most large cities. One version works as follows: you choose one of the 1000 three‑digit numbers 000 to 999 and pay your local numbers runner a dollar to enter your bet. Each day, one three‑digit number is chosen at random and pays off $600 . The law of large numbers tells us what happens in the long run. Like many games of chance, the numbers racket has outcomes that vary considerably—one three‑digit number wins $600 and all others win nothing—that gamblers never reach “the long run.” Even after many bets, their average winnings may not be close to the mean. For the numbers racket, the mean payout for single bets is $0.60 ( 60 cents) and the standard deviation of payouts is about $18.96 . If Joe plays 350 days a year for 40 years, he makes 14,000 bets. Unlike Joe, the operators of the numbers racket can rely on the law of large numbers. It is said that the New York City mobster Casper Holstein took as many as 25,000 bets per day in the Prohibition era. That's 150,000 bets in a week if he takes Sunday off. Casper's mean winnings per bet are $0.40 (he pays out 60 cents of each dollar bet to people like Joe and keeps the other 40 cents). His standard deviation for single bets is about $18.96 , the same as Joe's.

(a) What is the mean of Casper's average winnings ?¯ on his 150,000 bets? (Enter your answer as dollars rounded to two decimal places.)

mean of average winnings=

What is the standard deviation of Casper's average winnings ?¯ on his 150,000 bets? (Enter your answer as dollars rounded to three decimal places.)

standard deviation=$

(b) According to the central limit theorem, what is the approximate probability that Casper's average winnings per bet are between $0.30 and $0.50 ? (Enter your answer rounded to four decimal places.)

approximate probability=

One way of making a series stationary is?

Overview

The SPSS output tables below are all based on a larger study of product assessments for an ecologically friendly engine oil. Participants saw the packaging of an ecologically friendly engine oil on their computer screen and were asked several questions regarding how they perceived this product. The tables below focus on only a few of the variables used in the study.

Coding

Gender was coded as 1=female and 2=male

PWOP_M_S refers to perceived warmth of product. Participants were asked to which extent they perceived the product as “warm.” The assumption is that the perception of the color of the product’s packaging influences this assessment. For this Chapter 11 exercise, I performed a median split on the variable. Thus, the variable is now dichotomous with 1=low perceived warmth and 2=high perceived warmth.

FLUEN_M_S refers to processing fluency. Participants were asked to which extent they perceived the product and its packaging as easy to process, well organized, logical, etc. For this Chapter 11 exercise, I performed a median split on the variable. Thus, the variable is now dichotomous with 1=low fluency and 2=high fluency.

A_PI refers to purchase intentions. This variable is continuous on a scale from 1 to 7. Higher values represent higher purchase intentions.

Note 1: It may be true that you are not fully familiar with the constructs and do not know much about the study context, but you can nevertheless interpret the results provided in a table from a statistical point of view.

Note 2: When responding to the questions, please provide your answers in a way which will encourage the reader to believe that you understood the logic of these statistical tests. For example, it is helpful to point out which numbers in the tables are important, and what the meaning of these numbers is.

Question 11.1

The following two tables are equivalent to Exhibit 11.10 in your textbook (Crosstab Chi-Square example).

Please provide an interpretation of the two tables. What are the insights we can obtain from the SPSS output shown below? What is the meaning of the “count” vs. the “expected count” information in the table? (explain the logic with an example from the table). What is the logic of the Chi Square tests (and specifically, what is the meaning of the numbers shown in the “Asymp. Sig” column?