Part 1. Difference in Means (Two Sample) Test 1) A random sample of 53 Australia
ID: 3231727 • Letter: P
Question
Part 1. Difference in Means (Two Sample) Test
1) A random sample of 53 Australian men yields a mean of 524 (on a measure of socio-economic standing in which a higher score means higher socio-economic standing) and a standard deviation of 115.49. A random sample of 107 Australian women has a mean of 489 with a standard deviation of 84.38. Can we infer that the population mean socio-economic standing of men is higher than the population mean for women?
Follow the 5-step model of hypothesis testing when writing your answer; you can set the alpha level as =0.05.
Part 2. Association between Two Variables Measured at Interval/Ratio Level
1) Mary computed the correlation between two variables. She found that the correlation is moderately strong and positive, r = .38. This association is based on 30 subjects selected at random. Mary wants to know at =0.05 if this correlation is significantly different from 0. Use your 5-steps for hypothesis testing procedure to answer this question.
2)The variables below were collected from a random sample of 10 precincts during the last national election.
A. Graph the association between voter turnout (this is the % of registered voters who voted in the election) and % of the total votes that went to Democratic party using a scattergram (also called a scatterplot).
B. Describe the direction of the association, whether the association appears linear, and identify whether there are any outliers.
C. Political scientists often predict that high voter turnout favors Democratic candidates. Calculate the sample correlation, r, then, using =0.05 and our 5-steps for hypothesis testing, determine whether this sample supports this hypothesis.
Voter Turnout (X)
% of Vote
Democratic (Y)
Voter Turnout (X)
% of Vote
Democratic (Y)
(x - x) (x - x)^2 y-) (y - )^2 (x - x)(y - ) 56 50 55 45 52 56 60 78 89 55 75 85 64 62 45 33 62 25 36 49Explanation / Answer
H0: 1 = 2
Ha: 1 > 2
=0.05
Test method. Two-sample right tailed t-test to determine whether the difference between means found in the sample is significantly different from the hypothesized difference between means.
Standard error, SE = sqrt[ (s12/n1) + (s22/n2) ] = sqrt[(115.492/53) + (84.382/107)] = 17.838194
Degrees of freedom, DF = (s12/n1 + s22/n2)2 / { [ (s12 / n1)2 / (n1 - 1) ] + [ (s22 / n2)2 / (n2 - 1) ] }
= (115.492/53 + 84.382/107)2 / {[(115.492/53)2/52] + [(84.382/107)2/106]} = 80.38
Test statistic, t = [ (x1 - x2) - d ] / SE = [(524-489) - 0]/17.838194 = 1.962082
p-value = 0.0266 < 0.05, result is significant, There is sufficient evidence to suggest that population mean socio-economic standing of men is higher than the population mean for women and therefore we reject the null hypothesis.
Note: Please post the remaining questions separately if they require solving