C) From Health Canada, the latest statistics on COPD rates show that for 2013, t

Question

C)        From Health Canada, the latest statistics on COPD rates show that for 2013, the annual national rate is 4% and that the provinces with the lowest rates are Manitoba and Saskatchewan at 2.8% and 2.9%, respectively.

Here in Ontario, our Minister of Health wants an updated estimate for the province. We know that the Ontario estimate will be very close to the national number so using this figure, and using the 95% confidence for our estimate and a reasonable acceptable error of 0.5%, how many people must be surveyed? (4)

Now using the results of (a), a survey was conducted and it was found that 206 people in the sample had COPD. From this result, test the claim at 95% confidence that the result from Ontario was different from that of the national average.

State the Null and Alternative Hypothesis (1)

Prepare the PDF and state the Decision Rule (1,1)

Compute the test statistic (2)

What is the decision (1)

What is your interpretation? (1)

What is the P-value? (2)

From the sample information of part (b), determine the 95% confidence interval. Does this support your decision/conclusion from part (b)? Explain. (2,1)

Is it possible to state that the current rate for Ontario is even smaller than the posted rates for Manitoba and Saskatchewan in 2013? That is, Ontario had the lowest COPD rate in the country. Explain (1,1)

Explanation / Answer

(a) reasonable accpetable error = 0.5%

confidence interval = 0.95

let say sample size = n

estimate rate for>

Margin of error = critcal test statistic * standard error of the proportion

0.005 = Z95% * sqrt [0.04 * 0.96/n]

0.005 = 1.96 * sqrt [0.04 * 0.96/n]

n = 5900

(b) Now sample size must be kept = 5900

the ontario estimaate p^ = 206/5900 = 0.0349

State the Null and Alternative Hypothesis

Ho : p = 0.04

Ha : p 0.04

standard error of the proportion se0 = sqrt [po * (1-p0)/N] = sqrt [0.04 * 0.96/ 5900] = 0.00255

95% confidence interval = p^ +- Z96% se0

= 0.0349 +- 1.96 * 0.00255

= 0.0349 +- 0.0050

= (0.0299, 0.0399)

Test Statistic

Z = (0.0349 - 0.04)/0.00255 = -2

P- value = 2 * Pr(Z < -2) = 2 * 0.0228 = 0.0456

Our decision is to reject the null hypothesis and can concude that proporton for ontario is different from national average. Both COnfidence interval and hypothesis testing prove same result.

as lowest limit of confidence interval is 0.0299 which is way above Manitoba and Saskatchewan proportion. So, Ontario can't the lowest COPD rate in the country.

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