In this exercise we examine the effect of the sample size on the significance te

Question

In this exercise we examine the effect of the sample size on the significance test for comparing two proportions. In each case suppose that p1 = 0.5 and and take n to be the common value of n1 and n2. Use the z statistic to test versus the alternative Compute the statistic and the associated P-value for the following values of n: 30, 40, 70, 90, 390, 490, and 990. Summarize the results in a table. (Test the difference p1 p2. Round your values for z to two decimal places and round your P-values to four decimal places.)p2 = 0.4,H0: p1 = p2Ha: p1 p2. Please show work and formula, NOT an excel or other app formula.

Explain what you observe about the effect of the sample size on statistical significance when the sample proportions p1 and p2 are unchanged. Which one is the correct answer?

___ As sample size increases, the test becomes less significant.

___ As sample size increases, the test becomes more significant.    

___ As sample size increases, there is no effect on significance.

__ There is not enough information.

Which one is the correct answer?

n z p-value 30 40 70 90 390 490 990

Explanation / Answer

here as we know thjat std error =(p1(1-p1)/n+p2(1-p2)/n2)1/2

also z stat =(p1-p2)/std error

from above formulas:

As sample size increases, the test becomes more significant.

please reply for any doubt

n std error z p-value 30 0.1278 0.7825 0.4339 40 0.1107 0.9035 0.3663 70 0.0837 1.1952 0.2320 90 0.0738 1.3553 0.1753 390 0.0354 2.8212 0.0048 490 0.0316 3.1623 0.0016 990 0.0222 4.4949 0.0000

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