Question

In november of 1997, austrialians were asked if they thought unemployment would increase. At the time 284 out of a random sample of 631 said that they thought unemployment would increase ("morgan gallup poll,"2013). Estimate the proportion of Austrialians in November 1997 who believed unemployment would increase using a 95% confidence interval.

A) Name of the interval

B) State the random variable and the parameter in words.

C) State and check the assumptions for hypothesis test

D) Find the sample statistics and the confidence interval. Label everything with letters and write the interval as an inequality

E) Statistical Interpretation

F) Real world Interpretation

G) Conclusion:

H) Interpretation:

Answer 1

Answer :

a)

To name the interval

Here it is of 95% confidence interval for extent of Australians in 1997 who accept that joblessness would increment.

b)

To state that the random variable & the parameter in words

Random variable : number of Australians who accept that joblessness would increment.

Parameter : Population extent of Australians in 1997 who accept that joblessness would increment.

c)

To state & check the assumption for a hypothesis test

let us consider the assumptions are given as follows

np > 5 and n(1-p) > 5

Now ,

np = 284

n(1-p) = 631- 284

= 347

Here we observe that both are greater than 5

So that the assumptions are satisfied .

d)

To give the statistics

x = 284

n = 631

p^ = 0.45

Here z value at 95% confidence interval is 1.96

Standard error , s = sqrt(p^(1-p^)/n)

= sqrt(0.45(1-0.45)/631)

SE = 0.0198

Now 95% confidence interval is given as follows

= p^ +/- z*SE

substitute values

= 0.45 +/- 1.96*0.0198

= 0.45 +/- 0.0388

= (0.4188 , 0.4888)

Hence the 95% confidence interval for proportion is 0.41 p 0.49

e)

Statistical interpretation

Here there is 95% confident that the true proportion of Australians who believe that jobless would raised is between 0.41 to 049 or 41.18% to 48.88%

f)

Real world interpretation

There is 95% of chance that the proportion of Australians who believe that jobless would increase is 45% with +/- 4%  

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