Question

*USA Today* ("Hybrid Car Sales Rose 81% Last Year," April
25, 2005) reported the top five states for sales of hybrid cars in
2004 as California, Virginia, Washington, Florida, and Maryland.
Suppose that each car in a sample of 2004 hybrid car sales is
classified by state where the sale took place. Sales from states
other than the top five were excluded from the sample, resulting in
the accompanying table.

State | Observed Frequency |
---|---|

California | 255 |

Virginia | 56 |

Washington | 37 |

Florida | 33 |

Maryland | 33 |

Total |
414 |

(The given observed counts are artificial, but they are
consistent with hybrid sales figures given in the article.)

The 2004 population estimates from the Census Bureau web site are
given in the accompanying table. The population proportion for each
state was computed by dividing each state population by the total
population for all five states. Use the *χ*^{2}
goodness-of-fit test and a significance level of

*α* = 0.01

to test the hypothesis that hybrid sales for these five states are proportional to the 2004 population for these states.

State | 2004 Population | Population Proportion |
---|---|---|

California | 35,842,038 | 0.495 |

Virginia | 7,481,332 | 0.103 |

Washington | 6,207,046 | 0.085 |

Florida | 17,385,430 | 0.240 |

Maryland | 5,561,332 | 0.077 |

Total |
72,477,178 |

Let *p*_{1}, *p*_{2},
*p*_{3}, *p*_{4}, and
*p*_{5} be the actual population proportions of 2004
for the five states in the following order: California, Virginia,
Washington, Florida, Maryland.

State the null and alternative hypotheses.

*H*_{0}: *p*_{1} =
*p*_{2} = *p*_{3} =
*p*_{4} = *p*_{5} = 0.2

*H*_{a}: *H*_{0} is not
true.

*H*_{0}: *p*_{1} =
*p*_{2} = *p*_{3} =
*p*_{4} = *p*_{5} = 0.495

*H*_{a}: *H*_{0} is not
true.

*H*_{0}: *p*_{1} =
*p*_{2} = *p*_{3} =
*p*_{4} = *p*_{5} = 414

*H*_{a}: *H*_{0} is not
true.

*H*_{0}: *p*_{1} = 0.495,
*p*_{2} = 0.103, *p*_{3} = 0.085,
*p*_{4} = 0.240, *p*_{5} =
0.077

*H*_{a}: *H*_{0} is not
true

.*H*_{0}: *p*_{1} = 204.93,
*p*_{2} = 42.642, *p*_{3} = 35.19,
*p*_{4} = 99.36, *p*_{5} =
31.878

*H*_{a}: *H*_{0} is not
true.

Calculate the test statistic. (Round your answer to two decimal
places.)

*χ*^{2} =

What is the *P*-value for the test? (Round your answer to
four decimal places.)

*P*-value =

What can you conclude?

Reject *H*_{0}. There is not enough evidence to
conclude that hybrid sales are not proportional to population size
for the five states listed.

Do not reject *H*_{0}. There is not enough
evidence to conclude that hybrid sales are not proportional to
population size for the five states listed.

Do not reject *H*_{0}. There is convincing
evidence to conclude that hybrid sales are not proportional to
population size for the five states listed.

Reject *H*_{0}. There is convincing evidence to
conclude that hybrid sales are not proportional to population size
for the five states listed.

Answer #1

a) Correct answer:

H0: p1 = 0.495, p2 = 0.103, p3 = 0.085, p4 = 0.240, p5 =
0.077

Ha: H0 is not true

b) From the given data

Observed | Expected | |||

Freq (Oi) | Probability | Freq. (Ei) | (Oi-Ei)^2 /Ei | |

California | 35842038 | 0.495 | 35876203.1 | 32.5356 |

Virginia | 7481332 | 0.103 | 7465149.33 | 35.0802 |

Washington | 6207046 | 0.085 | 6160560.13 | 350.7694 |

Florida | 17385430 | 0.240 | 17394522.7 | 4.7531 |

Maryland | 5561332 | 0.077 | 5580742.71 | 67.5135 |

Total: | 72477178 | 72477178 | 490.6518 |

Degrees of freedom: 5-1 = 4

**Test Statistic, X^2: 490.6518**

c) **P-Value: 0.0000**

since P-value < alpha 0.01 so we reject H0

Correct answer: Option (D) Reject *H*_{0}. There
is convincing evidence to conclude that hybrid sales are not
proportional to population size for the five states listed.

USA Today ("Hybrid Car Sales Rose 81% Last Year," April
25, 2005) reported the top five states for sales of hybrid cars in
2004 as California, Virginia, Washington, Florida, and Maryland.
Suppose that each car in a sample of 2004 hybrid car sales is
classified by state where the sale took place. Sales from states
other than the top five were excluded from the sample, resulting in
the accompanying table.
State
Observed Frequency
California
255
Virginia
56
Washington
37
Florida...

The authors of a paper studied a random sample of 355 Twitter
users. For each Twitter user in the sample, the "tweets" sent
during a particular time period were analyzed and the Twitter user
was classified into one of the following categories based on the
type of messages they usually sent.
Category
Description
IS
Information sharing
OC
Opinions and complaints
RT
Random
thoughts
ME
Me now
(what I am doing now)
O
Other
The accompanying table gives the observed counts...

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