PSYC/SOCI 3381 Statistics for Behavioral Sciences

Instruction:

Please show all your work as much as you can.

Question 1 You are conducting a study to test whether there is a difference in the mean number of alcoholic drinks consumed per evening between the following groups: freshmen who live on campus (sample 1) and freshmen who live off campus (sample 2). Your results will be presented to the Dean of Students so that safety tips and prevention measures can be implemented for the appropriate groups. For freshmen who live on campus (N = 25), their mean number of drinks is 6.2, and their standard deviation is 2. For freshmen who live off campus (N = 30), their mean number of drinks is 3.8, and their standard deviation is 1.

(a) (4pts extra) Please identify independent variable and dependent variable.

(b) (5pts) Please write the research hypothesis and null hypothesis for this question (note: make sure it is the two-tailed test)

(c) (4pts) Which test statistic should you use? (e.g., two sample independent T-test, ANOVA, chi-square, or correlation)?

(d) (10 pts) Compute the appropriate test statistic (Note: please show all your work)

(e) (10pts) In full sentences, please make a decision AND interpret your results when = .05 for a two-tailed test. In your answer, please include critical test statistics from the proper distribution chart.

Question 2 Students in a large lecture class want to know who has, on average, more Facebook friends, male or female students. Summary statistics are available in the provided table. We are testing if this sample provides evidence of significantly more Facebook friends for male than female students at this university.

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Gender N (sample size) x (mean) S (standard deviation)

Male 68 678.9 317.6

Female 91 616.1 330.6

(a) (4 extra points) Please identify independent variable and dependent variable in this research.

(b) (4pts) Please write the research hypothesis and null hypothesis for this question under ONE-TAILED TEST.

(c) (4pts) Which test statistic should you use? (e.g., two sample independent T-test, ANOVA, chi-square, or correlation)?

(d) (10 pts) Compute the appropriate test statistic (Note: please show all your work as much as you can)

(e) (10pts) In full sentences, please make a decision AND interpret your results when = .05 for a one-tailed test. In your answer, please include critical test statistics from the proper distribution chart.

(Question 3- Question 4) The sampling distribution shows sample means from samples of size n = 50.

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59 61 63 65 67 69 71

Question 3 (3pts).What does one dot on the sampling distribution represent

Question 4 (3pts). Please answer the estimated population mean from the dotplot above.

Question 5 (3pts). Which of the following is true of the sampling distribution of means?

a. The sampling distribution of means approximates the normal curve.

b. The mean of a sampling distribution of means is equal to the population mean.

c. The standard deviation of a sampling distribution of means is smaller than the standard deviation of the population.

d. all of the above

Question 6 (3points). The standard error of the difference between means:

a. cannot be properly estimated.

b. requires only one sample's characteristics.

c. is an estimate of the standard deviation in a sampling distribution of differences.

d. does not include the sample sizes

Question 7 (3points). The larger the value of our obtained t:

a. the more probable that our results are due to chance alone.

b. the less probable that our results are due to chance alone.

c. the larger our critical t value.

d. the larger the probability of making a Type I error.

Question 8 (3points) When we test hypotheses of differences between means, we:

a. compare our results to that of a probability distribution.

b. test to see if our obtained difference could have happened by chance.

c. calculate a type of z score to locate our difference on a probability distribution.

d. All of the above are correct.

Question 9 (3points) Compared to the .05 level of significance, the .01 level of significance:

a. means a higher probability of the obtained difference being a result of sampling error.

b. means a lower probability of the obtained difference being a result of sampling error.

c. means a perfectly normal distribution.

d. means a skewed distribution.

Question 10(3 points for each). Identify each of the following as either a parameter or a statistic. (If you add a correct statistical notation corresponding to your answer, 4 extra credits will be given).

1) Average commute time for employees at a small company, based on interviews with all employees.

a) Statistics b) Parameter

2) Proportion of students at a university that are part-time, based on data on randomly selected students enrolled at the university.

a) Statistics b) Parameter

Question 11 (4pts) How is a confidence interval related to a point estimate?

a. Whenever we cannot calculate an interval, the confidence interval is equal to the point estimate.

b. The point estimate is the starting point of the interval.

c. The point estimate is the midpoint of the interval.

d. The point estimate is the ending point of the interval.

Question 12. (12pts). Adopting a Child in the US

A survey of 1,000 American adults conducted in January 2013 stated that "44% say it's too hard to adopt a child in the US." The survey goes on to say that "The margin of sampling error is +/- 3 percentage points with a 95% level of confidence."

a) (3pts) What is the relevant sample statistic?

b) (3pts) What population parameter are we estimating with this sample statistic?

c) (3pts) Use the margin of error to give a confidence interval for the estimate.

d) (3pts) Is 0.42 a plausible value of the population proportion? Is 0.50 a plausible value?

Question 13 (4pts) Please generate your own research question that needs to be tested using two sample independent T test. Then, write the null and research hypothesis. Also specify one-tailed or two-tailed test (Please see exemplar answers below)

Example: research question: are there any differences in GPA between male and female college students? or do female students have a higher GPA than male students?

Research hypothesis (H1)

• There are differences in the mean of GPA between male and female students (two-tailed test)
• Female students have a higher mean of GPA than male students (one-tailed test)

Null hypothesis (H0)

• There is no difference in the mean of GPA between male and female students (two-tailed test)
• Female students have lower GPA than male students or same (one-tailed test)