which test should I use t or z and why? I try to use t-test but can\'t find the

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which test should I use t or z and why? I try to use t-test but can't find the correct p-value as the only thing I can use to check is the distribution table. Thank you!!!

3) The proportion of people who love dogs is known to be 75 % Australia wide. A town in far north Queensland is often different in many aspects to the rest of Australia. When C families were sampled the proportion who loved dogs was 68%. (If C happens to be zero, you may assume C to be 10) a) Test whether this town is significantly different to the rest of Australia, given the probability of making a type 1 error is 5%. Use critical value for testing the hypothesis. Be sure to interpret your answer (6 marks) b) What is the p-value? (1 mark)

Explanation / Answer

(a)

Data:    

n = 10   

p = 0.75   

p' = 0.68   

Hypotheses:    

Ho: p = 0.75   

Ha: p 0.75   

Decision Rule:    

= 0.05   

Lower Critical z- score = -1.9600   

Upper Critical z- score = 1.9600   

Reject Ho if |z| > 1.9600   

Test Statistic:    

SE = {p (1 - p)/n} = (0.75 * (1 - 0.75)/10) = 0.1369

z = (p'- p)/SE = (0.68 - 0.75)/0.136930639376292 = -0.5112

Decision (in terms of the hypotheses):

Since 0.5112 < 1.9600 we fail to reject Ho

Conclusion (in terms of the problem):    

There is no sufficient evidence that the proportion is different from 0.75

(b) p- value = 0.6092

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