Question

Suppose there is a random sample of n observations, divided into four groups. The table below summarizes the count of observations that were seen in each group.

Group 1 -36

Group 2 -30

Group 3 -68

Group 4 -45

We are interested in testing the null hypothesis H0:p1=p2=p3=p4=0.25, against the alternative hypothesis HA:Atleastoneproportionisincorrect.

What is the expected count for each of the groups? Expected: _______

What is the value of the test statistic? _______Round your response to at least 2 decimal places.

What are the appropriate degrees of freedom? _______

What is the P-value? _______ Round to at least 4 decimal places

Answer #1

The null and alternative hypothesis is

H0: p1 = p2 = p3 = p4 = 0.25

HA:Atleast one proportion is incorrect.

Level of significance = 0 .05

Test statistic is

O: Observed frequency

E: Expected frequency.

E = n*pi

O | E | (O-E) | (O-E)^2 | (O-E)^2/E | |

36 | 44.75 | -8.75 | 76.5625 | 1.710894 | |

30 | 44.75 | -14.75 | 217.5625 | 4.861732 | |

68 | 44.75 | 23.25 | 540.5625 | 12.07961 | |

45 | 44.75 | 0.25 | 0.0625 | 0.001397 | |

Total | 179 | 18.65 |

Degrees of freedom = Number of E's - 1 = 4 - 1 = 3

P-value = P( ) = 0.0003

P-value < 0.05 we reject null hypothesis.

Conclusion:

Atleast one proportion is incorrect.

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