Hi there,

I actually got a different result for part c).

I calculated the p-value using R:

prop.test(755, 1000, 0.8, alternative = "greater", correct = F)

which gave a p-value = 0.9998. Thus, the p-value greater than 0.05.

Based on this, I would retain the null hypothesis and conclude that there is not enough evidence that the true proportion of Australians agreeing with the economist's prediction is significantly more than 0.8 at 5% significance.

Below a couple screenshots.

Could you explain where I made a mistake?

Thanks in advance!

c) Conduct a hypothesis test to determine if the true proportion of Australians agreeing with the economist's prediction is more than 0.80 at the 5% level of significance. [6 marks] p-value method Test used: Since the data is qualitative and has one group of 1000 Australians surveyed, we will do a one sample Z-test of proportion. Test statistic and sampling distribution: Zobs = p- P Vp(1-p) ~N(0,1) Hypotheses: Ho : p = 0.8 H1 : p > 0.8 Significance: a = 5% = 0.05 Decision Rule: We will reject Ho if the p-value is less than a = 0.05. Calculations: R script: prop.test(755, 1000, 0.8, alternative = "greater", correct = F) R commander output: 1-sample proportions test without continuity correction data: 755 out of 1000, null probability 0.8 X - squared = 12.656, df = 1, p-value = 0. 9998 alternative hypothesis: true p is greater than 0.8 95 percent confidence interval: 0. 7319606 1. 0000000 sample estimates: P 0. 755 The p-value is 0.9998. Decision: p = 0.9998 > a = 0.05 Since the p-value (0.9998) is greater than 0.05, we will retain Ho. Conclusion:Since we retained the null hypothesis, there is not enough evidence that the true proportion of Australians agreeing with the economist's prediction is significantly more than 0.8, at the 5% level of significance. critical value method Test used, Test statistic and sampling distribution, Hypotheses, Significance as above. Decision Rule: We will reject Ho if Zobs > Zacit- Zarit = Zo.05 From the normal tables, Zo.os is not stated. Calculate Zo.os by using Zo.0495 and Zo.0sos and take average of the two. Zarit = Zo.05 = [(-1.64) + (-1.65)] / 2 = -1.645 We will reject Ho if Zobs > -1.645. Calculations: n = 1000 Sample proportion: p = 0.755 True population proportion: p = 0.80 Zobs = p - P 0.755 - 0.80 Vp(1-p) V0.80(1-0.80)/1000 -0.045 0.01264911 = -3.5576 The observed value for the test statistic is Zobs = =3.5576 Decision: Zobs = -3.5576