Question

On the island of Lilliput, a sample random sample of 500 people reveals that 450 of them prefer to open their egg on the small end. On the island of Blefuscu, a sample random sample of 1000 people reveals that 875 of them prefer to open their egg on the small end.

Part One:
What is the sample proportion of Lilliputians who prefer to open their egg on the small end (exact)?

What is the sample proportion of Blefuscuans who prefer to open their egg on the small end (exact)?

What is the pooled sample proportion (to six decimal places): -----

What is the pooled standard error (to six decimal places): ----


Part Two:
Assuming that Lilliputians and Blefuscuans are equally likely to open their egg on the small end, what is the probability of selecting samples of these sizes with the sample proportion being as much higher for Lilliputians as it was for our samples (i.e., one-sided p-value, to four decimal places):

The above p-value comes from a test-statistic of z=  (enter number without sign).

Answer 1

sample proportion of Lilliputians

sample proportion of Blefuscuans

pooled sample proportion

Q=1-P = 1-0.883333 = 0.116667

pooled standard error:

Part 2)

Hypothesis:

Ho: P1 = P2

Ha: P1 > P2

Test statistic:

P-value: 0.0775 ................Using standard Normal table

P-value > , i.e. 0.0775 > 0.05, That is Fail to Reject Ho at 5% level of significance.

Therefore, there is Not sufficient evidence to conclude that, the sample proportion being as much higher for Lilliputians as it was for our samples.