Question

eCoach Step 3: Mean 4 LabAssignment#3 Z-tests and T-tests Note: Be sure to read and answer each question carefully, label and highlight your answers with the correct number/letter, and show all your work. FOLLOW THE TEMPLATE 1) Below are depression scores for women who report experiencing intimate partner violence. These scores were taken from a random sample of 10 women. In the general population, depression scores are normally distributed with a mean (μ) of 21 and a standard deviation (o) o12. You hypothesize that this sample is not representative of the general population. Specifically. you hypothesize that these women form a distinct sub-population, with specifically HIGHER depression, relative to the general population. That is, if they have lower depression, that would be treated the same as having the same amount of depression. Conduct a one-sample z-test by answering the following questions. Data: 23, 26, 24, 19, 25, 20, 26, 23, 20, and 24 a. State the null and alternative hypotheses b. Are you going to be using a one- or two-tailed test? Explain the reason for your choice. c. Find the corresponding critical z-value for Type I error rate (alpha) of a- o.05. d. Calculate your observed z-statistic. e. Compare your observed z-statistic to the critical z-value. What do you conclude regarding the null hypothesis f. Calculate and interpret the standardized effect size (Cohen's d). g. What do you conclude about your research question (use your own words, in everyday language) 2) Below is the data for a personality questionnaire measuring conscientiousness. These data were

Answer 1

$Let~\mu=true~mean~depression~score.\\ a.~Null~hypothesis,~H_0:\mu=21\\ Alternative~hypothesis,~H_1:\mu>21.\\ b.~Since~H_1:\mu>21,~so~we~are~going~to~use~one~tail~(right-tail)~test.\\ c.~Critical~z-value=1.6449\\ d.~\bar{x}=\frac{1}{10}\sum_{i=1}^{10} x_i=(23+26+24+19+25+20+26+23+20+24)/10\\ =23\\ Observed~z-statistic=(\sqrt{10}\times( 23-21))/2=3.1623\\ e.~Since~Observed~z-statistic>Critical~z-value,~so~we~reject~H_0~at~5\%~level~of~significance.\\ f.~Cohan's~d=( 23-21)/2=1\Rightarrow Large ~effect ~size.\\ g.~Our~hypothesis~is~correct~i.e.~these~women~form~a~district~sub-population~with~specifically\\ higher~depression~relative~to~the~general~population.$