Question

Among the four northwestern states, Washington has 51% of the total population, Oregon has 30%, Idaho has 11%, and Montana has 8%. A market researcher selects a sample of 1000 subjects, with 450 in Washington, 340 in Oregon, 150 in Idaho, and 60 in Montana. At the 0.05 significance level, test the claim that the sample of 1000 subjects has a distribution that agrees with the distribution of state populations.

Answer #1

The null and alternate hypothesis are:

H0: Sample has distribution that agrees with distribution of state populations.

Ha: Sample has distribution that does not agree with distribution of state populations.

Observed (Oi) | Expected (Ei) | ||

Washington | 450 | 0.51(1000)=510 | 7.06 |

Oregon | 340 | 0.30(1000)=300 | 5.33 |

Idaho | 150 | 0.11(1000)=110 | 14.55 |

Montana | 60 | 0.08(1000)=80 | 5 |

TOTAL | 1000 | 1000 | 31.94 |

Test statistic value =

The critical value is given by:

Since the test statistic value is greater than the critical value, so we have sufficient evidence to reject null hypothesis H0. Thus, we can say that sample has distribution that does not agree with distribution of state populations.

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