CLASSICAL INFERENCE: HYPOTHESIS TES TING 242 en-in (b) There was no control grou

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CLASSICAL INFERENCE: HYPOTHESIS TES TING 242 en-in (b) There was no control group- a group that received no inspired oxyge this study. What is the implication of this? 13 In the remark on page 220, we indicated that is not common to use a continuitv correction when using the normal approximation to the two-sample proportions test. Use simulation to explore the sampling distribution of the Z statistic, for (a) p = 0.5, n = 10, n2 = 10, (c) p = 0.5, ni = 10, n2 = 12, (d) p = 0.5, ni = 10, n2 = 15, t) p 0.5, ni 10. n2her com ations al Desc ial to the nth, (e) your choice of four other combinations of p, ni, and n2. In all cases, use at least 10 replications and create normal quantile plots with the option pch". " (for better resolution). Describe the distributions. 14. A pharmaceutical company is conducting a clinical trial to determine the effec- tiveness of a new drug to lower cholesterol levels. If denotes the mean change (before-after) in cholesterol levels, they will test Ho: = 0 versus HA: Describe the Type 1 and Type errors that could be made and the practic

Explanation / Answer

Solution

Let X = Number of people in the age group 18-29 years who say yes to the question whether there is evidence of global warming.

and Y = Number of people in the age group 31-35 years who say yes to the question whether there is evidence of global warming.

Then, X ~ B(n1, p1), and Y ~ B(n2, p2) where n1 and n2 are sample sizes and p1 = probability that a person in the age group 18-29 years who say yes to the question whether there is evidence of global warming and p2 = probability that in the age group 31-35 years who say yes to the question whether there is evidence of global warming, which in turn are also equal to the proportion of     in the population.

Claim : Higher proportion of younger people believe there is evidence of global warming.

Hypotheses:

Null H0 : p1 = p2   Vs HA : p1 > p2

Test Statistic:

Z = (p1cap – p2cap)/[pcap(1 - pcap){(1/n1) + (1/n2)} where p1cap and p2cap are sample proportions, n1, n2 are sample sizes and pcap = {(n1 x p1cap) + (n2 x p2cap)}/(n1 + n2).

Calculations:

p1cap = 126/197 = 0.6396

p2cap = 223/406 = 0.5493

pcap = (126 + 223)/(197 + 406)

         = 349/603

         = 0.5788

(1 - pcap) = 0.4212

(1/n1) = 1/197 = 0.0051

(1/n2) = 1/406 = 0.0025

{(1/n1) + (1/n2)} = 0.0076

Substituting these values, Zcal = 2.098

Distribution, Critical Value and p-value:

Under H0, distribution of Z can be approximated by Standard Normal Distribution

So, given a level of significance of %, Critical Value = upper % of N(0, 1), and

p-value = P(Z > Zcal)

Using Excel Functions of N(0, 1), and taking = 5, Critical Value = 1.645 and p-value =

P(Z > 2.098) = 0.018

Decision Criterion (Rejection Region):

Reject H0, if Zcal > Zcrit or if p-value < .

Decision:

Since Zcal > Zcrit, p-value < , H0 is rejected.

Conclusion :

There is enough evidence to suggest that the claim that 'higher proportion of younger people believe there is evidence of global warming' is valid.

DONE

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