Question

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?

Answer #1

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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