Statistics Question: Do these results give convincing evidence that showing the picture affects people’s opinions about free health care for those experiencing homelessness?

Question

A researcher asked 80 randomly selected people if free health care should be provided to people experiencing homelessness. Half of the respondents (40), determined at random, were shown a picture of a homeless woman with a small child. When shown the picture 67.5% agreed that free health care should be provided to the homeless. When the picture was not shown, only 45% agreed with tis statement. Do these results give convincing evidence that showing the picture affects people’s opinions about free health care for those experiencing homelessness?

Write out P-hat1 and P-hat2

The Standard error

The conditions

The Null and alternate hypotheses (also the parameter)

The Test statistic and p-value

The Conclusion.

Answer 1

Hello,

p^1 = probability people shown picture will say yes = 0.675

p^2 = probability people not shown picture will say yes = 0.45

p^ Total = (0.675*40) + (0.45*40) / 80 = 0.5625

q^ = 1 - p^Total = 0.4375

Standard Error = sqrt (p^q^(1/n1 + 1/n2))

n1= 40; n2 = 40

SE = sqrt(0.5625*0.4375((1/40)+(1/40)) = 0.111

Conditions:

Independence is assumed; randomness is given; population size is assumed to be more than 10*80--a lot more than 800. Numbers of "successes," people advocating for free health care--and "failures"--those advocating against--both exceed 10. All reasonable conditions for inference are met.

H0: p1 = p2 (Picture has no effect on perception)

HA: p1 not equal to p2 (Picture affects perception. Note that no direction (i.e. positive or negative) was given here.

Test Statistic and p-value

Now, enter all data into TI-83 or 84 Plus-- STAT-TESTS-2PropZTest:

x1 = p^1*40 = 0.675*40 = 27

x2= p^2*40 = 0.45*40 = 18

n1= 40

n2= 40

p1 not equal to p2

z= 2.028

p= 0.043

Conclusion: Depends on significance level alpha, which was not given here. For alpha 0.05, you would reject the null and conclude viewing the picture has some effect on opinion. For alpha 0.01, you would fail to reject the null and conclude viewing the picture has no significant effect. I hope this helps.