In a recent study, subjects were shown pictures of a person smiling, One of thes

Question

In a recent study, subjects were shown pictures of a person smiling, One of these pictures showed a real smile, while the other showed a fake smile. A random sample of 64 subjects found that 40 were able to correctly choose the real smile. Is this evidence that the subjects were able to distinguish the smiles better than by a random guess (p=0.5)?

a) state the hypotheses

b) calculate the test statistic

c) calculate the significance probability or P value, as accurately as possible

d) give a conculsion in terms of strength of evidence against the null hypothesis

e) are the results statistically significant at alpa=0.05 level of signifiance? explain

f) describe briefly what would be a type ii error in this case

Explanation / Answer

a) null hypothesis: p=0.5 ;  subjects were not able to distinguish the smiles better than by a random guess

alternate hypothesis: p>0.5 ;subjects were able to distinguish the smiles better than by a random guess

std error =(p(1-p)/n)1/2 = 0.0625

phat =40/64 =0.625

hence test stat t=(phat-p)/std error =(0.625-0.5)/0.0625 =2

c) p value for above one tailed test =0.02275

d) p value gives probabilty of being null hypothessi true. Here as p value is very low , the strength of evidence against the null hypothesis is very high

e) as p value is lower then 0.05 level; results are significant and we can reject null hypothesis.

f)type II error would be not to reject Ho while it is false.

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