Question

# A Worker asked 76 interns to randomly pick a natural number from 1 to 5. Numbered...

A Worker asked 76 interns to randomly pick a natural number from 1 to 5.

Numbered Picked:

1=8 2=14 3=24 4=21 5=9

Does the data provide enough evidence at the 1% significance level, to show that the student's version of random selection is not the same as simple random sampling?

 Category Observed Frequency (O) Proportion, p Expected Frequency (E) (O-E)²/E 1 8 0.2 76 * 0.2 = 15.2 (8 - 15.2)²/15.2 = 3.4105 2 14 0.2 76 * 0.2 = 15.2 (14 - 15.2)²/15.2 = 0.0947 3 24 0.2 76 * 0.2 = 15.2 (24 - 15.2)²/15.2 = 5.0947 4 21 0.2 76 * 0.2 = 15.2 (21 - 15.2)²/15.2 = 2.2132 5 9 0.2 76 * 0.2 = 15.2 (9 - 15.2)²/15.2 = 2.5289 Total 76 1.00 76 13.3421

Ho: Proportions are same.

H1: Proportions are different.

Test statistic:

χ² = ∑ ((O-E)²/E) = 13.3421

df = n-1 = 4

Critical value:

χ²α = CHISQ.INV.RT(0.01, 4) = 13.2767

p-value:

p-value = CHISQ.DIST.RT(13.3421, 4) = 0.0097

Decision:

p-value < α, Reject the null hypothesis

There is enough evidence to conclude that the student's version of random selection is not the same as simple random sampling.

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