Essential Statistics for the Behavioral Sciences. Second Edition Chapter 9, #20: A study evaluating the effects of parenting style (authoritative, permissive) on child well-being observed 20 children (10 from parents who us an authoritative parenting style and 10 from parents who use a permissive parenting style). Children between the ages of 12 and 14 completed a standard child health questionnaire where scores can range between 0 and 100, with higher scores indicating greater well-being. The scores are given in the table. Authoritative Parenting Style: 60, 65, 70, 65, 80, 50, 75, 55, 60, and 70. Permissive Parenting Style: 80, 75, 55, 85, 90, 65, 70, 65, 70, and 80. [a] Test whether or not child health scores differ between groups using a 0.05 level of significance. State the value of the test statistic and the decision to retain or reject the null hypothesis. [b] Compute effect size using estimated Cohen's d.

A survey of Internet users reported that 22% downloaded music onto their computers. The filing of lawsuits by the recording industry may be a reason why this percent has decreased from the estimate of 30% from a survey taken two years before. Assume that the sample sizes are both 1431. Using a significance test, evaluate whether or not there has been a change in the percent of Internet users who download music. Provide all details for the test. (Round your value for z to two decimal places. Round your P-value to four decimal places.)

z =

P-value = 0 Correct:

Also report a 95% confidence interval for the difference in proportions. (Round your answers to four decimal places.) (_________,_________)

Explain what information is provided in the interval that is not in the significance test results.

The interval tells us there was a significant change in music downloads, but the test statistic is inconclusive.

The significance test does not indicate the direction of change, but the interval shows that the music downloads decreased.

The interval gives us an idea of how large the difference is between the first survey and the second survey.

The interval shows no significant change in music downloads. The interval does not provide any more information than the significance test would tell us.

3. Provide 5 examples of research studies with cross-sectional study design. What were the independent and dependent variables in each of these studies? Add references for each example.

4. Provide 5 examples of randomized controlled trials (RCTs). What were the independent and dependent variables in each of these studies? Add references for each example.

Essential Statistics for the Behavioral Sciences. Second Edition Chapter 10, #22: A clinical psychologist noticed that the siblings of his obese patients are often not overweight. He hypothesized that the normal-weight siblings consume fewer daily calories than the obese patients. To test this using a matched-pairs design, he compared the daily caloric intake of obese patients to that of a "matched" normal-weight sibling. The calories consumed for each sibling pair are given in the table. Normal-Weight Sibling: 1600, 1800, 2100, 1800, 2400, 2800, 1900, 2300, 2000, and 2050. Overweight Sibling: 2000, 2400, 2000, 3000, 2400, 1900, 2600, 2450, 2000, and 1950. [a] Test whether or not obese patients consumed significantly more calories than their normal-weight siblings at a 0.05 level of significance. State the value of the test statistic and the decision to retain or reject the null hypothesis. [b] Compute effect size using omega-squared. [c] Did the results support the researcher's hypothesis? Explain.

Task: Apply mathematical problem solving skills to a variety of problems at the college level.

To accomplish this task, the students will

1. Identify what they are given and what they need to find;

2. Identify the type of problem they have been given and the tools necessary to solve the problem;

3. Correctly apply the tools to the information given to set up the problem;

4. Perform mathematically correct calculations to determine a solution;

5. Interpret their results in terms of the original problem.

The written work for the following problem must be submitted to receive credit. The formulas and numbers that have been used in the formula must be shown to receive credit.

A local bank claims that the waiting time for its customers to be served is the lowest in the area. A competitor bank checks the waiting times at both banks. The sample statistics are listed below. Test the local bank’s claim. Use the information given below. State the null and alternative hypotheses, the significance level, the critical value, the test statistic, the decision and conclusion. All work must be written out and shown.

Sample statistics for a local bank and a competitor's bank

Local Bank Competitor Bank   

Sample size Local Bank: n1=46 , Competitor bank: n2=50

Average waiting time in minutes for each sample Local Bank: X¯1=2.3 mins. (line should be above X), Competitor Bank X¯1=2.6 mins.(line should be above X)

Sample Standard Deviation of each Sample Local BankL s1= 1.1 mins, Competitor Bank:s2=1.0 mins

1. Are the samples dependent or independent?
2. State your Null/Alternative hypotheses
3. What is the test-statistic?
4. What is the p-value?
5. What are the critical values?
6. Does the test-statistic lie in the rejection region?
7. Interpret the Result?
8. Does the result change for a different value of alpha? Explain?

*** Indicate if statement is true (T) or false (F), and explain why? ***

(a) A 95% prediction interval for a future observation at x0 is wider than the 95% confidence interval for the mean response at x0.

(b) For a simple linear regression model y = β0 + β1x + ε, and using a 95% confidence interval for the slope β1 (-0.0416, 0.8145), we can conclude in a 0.1 significance level that x and y are not significantly linearly related to each other.

(c) The coefficient of determination R^2 is always a good measure of comparison between two models.

(d) The estimator σ^2 = MSE has a normal distribution.

(e) A 95% confidence interval for the slope β1 will be wider if we have a sample size of n = 11 instead of n=7

(f) In a simple linear regression model, where the errors are independent and normally distributed, the least squares estimator β0 has a normal distribution also.

(g) The prediction is trustworthy even if we are in the region where the values of X are extrapolated.

(h) The residual is the difference between the observed value of the dependent variable and the predicted value of the dependent variable.

(i) If the p-value for testing H0 : β1 = 0 Vs H1 : β1 ̸= 0 is less than the significance levelα, then we reject the null hypothesis and conclude that there is no significant linear relationship between x and y.

A researcher knows from the past that the standard deviation of the time it takes to inspect a car is 16.8 minutes. A random sample of 24 cars is selected and inspected. The standard deviation is 12.5 minutes. At a= 0.05, can it be concluded that the standard deviation has changed? Use the P-value method. Assume the variable is normally distributed.

The file Hotel Prices contains the prices in British pounds (about US$ 1.52 as of July 2013) of a room at two-star, three-star, and four-star hotels in cities around the world in 2013.

a. Compute the mean, median, first quartile, and third quartile.

b. Compute the range, interquartile range, variance, standard de-viation, and coefficient of variation.

c. Interpret the measures of central tendency and variation within the context of this problem.

d. Construct a boxplot. Are the data skewed? If so, how?

e. Compute the covariance between the average price at two-star and three-star hotels, between two-star and four-star hotels, and between three-star and four-star hotels.

f. Compute the coefficient of correlation between the average price at two-star and three-star hotels, between two-star and four-star hotels, and between three-star and four-star hotels.

g. Which do you think is more valuable in expressing the relation-ship between the average price of a room at two-star, three-star, and four-star hotels—the covariance or the coefficient of cor-relation? Explain.

h. Based on (f), what conclusions can you reach about the relationship between the average price of a room at two-star, three-star, and four-star hotels?

For your study on the food consumption habits of teenage​ males, you randomly select 10 teenage males and ask each how many​ 12-ounce servings of soda he drinks each day. The results are listed below. At alphaequals0.05​, is there enough evidence to support the claim that teenage males drink fewer than three​ 12-ounce servings of soda per​ day? Assume the population is normally distributed. 3.4 2.8 2.3 2.8 1.9 3.7 2.8 3.6 3.7 1.7

write a program in matlab to produce a discrete event simulation of a switching element with 10 inputs and 3 outputs. Time is slotted on all inputs and outputs. Each input packet follows a Bernoulli process. In a given slot, the independent probability that a packet arrives in a slot is p and the probability that a slot is empty is (1– p). One packet fills one slot. For a switching element if 3 or less packets arrives to some inputs, they are forwarded to the switching element outputs without a loss. If more than 3 packets arrive to the inputs of the switching element, only 3 packets are randomly chosen to be forwarded to the switching element outputs and the remaining ones are discarded. In your simulation the program will mimic the operation of the switch and collect statistics. That is, in each time slot the program randomly generates packets for all inputs of the switching element and counts how many packets can be passed to the output of the switching element (causing throughput) and, alternatively counts how many packets are dropped (when the switching element has more than 3 input packets at a given time slot) . Your task is to collect throughput statistics for different values of p (p = 0.05, 0.1 up to 1.0 in steps of 0.05), by running the procedure described above for each value of p and for many slots (at least a thousand slots per value of p). The more simulated slots, the more accurate the results will be. Based on this statistics, plot two graphs: 1) the average number of busy outputs versus p, and 2) the average number of dropped packets versus p.

Total plasma volume is important in determining the required plasma component in blood replacement therapy for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. Suppose that a random sample of 41 male firefighters are tested and that they have a plasma volume sample mean of x = 37.5 ml/kg (milliliters plasma per kilogram body weight). Assume that σ = 7.70 ml/kg for the distribution of blood plasma.

(a) Find a 99% confidence interval for the population mean blood plasma volume in male firefighters. What is the margin of error? (Round your answers to two decimal places.)

(b) What conditions are necessary for your calculations? (Select all that apply.)

σ is known

σ is unknown

the distribution of weights is uniform

n is large

the distribution of weights is normal

(c) Interpret your results in the context of this problem.

99% of the intervals created using this method will contain the true average blood plasma volume in male firefighters.

The probability that this interval contains the true average blood plasma volume in male firefighters is 0.99.   

1% of the intervals created using this method will contain the true average blood plasma volume in male firefighters.

The probability that this interval contains the true average blood plasma volume in male firefighters is 0.01.

(d) Find the sample size necessary for a 99% confidence level with maximal margin of error E = 3.00 for the mean plasma volume in male firefighters. (Round up to the nearest whole number.)

A random sample of 77 eighth-grade​ students' scores on a national mathematics assessment test has a mean score of 264 with a standard deviation of 40.

This test result prompts a state school administrator to declare that the mean score for the​ state's eighth-graders on this exam is more than 260.

At a=0.09​, is there enough evidence to support the​ administration's claim? Complete parts​ (a) through​ (e).

HW9#8

Assume that the paired data came from a population that is normally distributed. Using a 0.05 significance level and

d=x−​y,

find d overbard​, s Subscript dsd​,

the t test​ statistic, and the critical values to test the claim that μd=0.

x 10 14 6 4 7 11 16 6

y 11 11 9 9 9 12 11 7

over score d=    (round three decimal places)

Sd= (Round three decimal places)

t= (round three decimal places)

Ta/2=pluse sign with a bar under it (round to three decimal places)

Conduct a hypothesis test (using either the p-Value Approach or the Critical Value Approach) to determine if the proportion of all recent clients is more dissatisfied than the traditional level of dissatisfaction. Use α = 0.08. Do not forget to include the correctly worded hypotheses and show all the steps required to conduct the hypothesis test. 92 out of sample of 200 were dissatisfied

The average income tax refund for the 2009 tax year was ​$3109. Assume the refund per person follows the normal probability distribution with a standard deviation of ​$917. Complete parts a through d below.

a. What is the probability that a randomly selected tax return refund will be more than $2000?

b. What is the probability that a randomly selected tax return refund will be between $1500 and $2900?

c. What is the probability that a randomly selected tax return refund will be between $3400 and 4000​?

d. What refund amount represents the 35th percentile of tax​ returns?