Question

1. An association of Christmas tree growers in Indiana sponsored a sample survey of Indiana households to help improve the marketing of Christmas trees. Respondents who had a tree during the holiday season were asked whether the tree was natural or artificial. Respondents were also asked if they lived in an urban area or in a rural area. Of the 410 households displaying a Christmas tree 160 lived rural area and 250 were urban residents. The tree growers want to know if there is a difference in preference for natural trees versus artificial trees between urban and rural households. Here is the data:

Population | n | Natural (X) |

Rural (1) | 160 | 62 |

Urban (2) | 20 | 86 |

a) Give the null and alternative hypotheses that are appropriate for this problem, assuming we have no prior information suggesting that one population would have a higher preference than the other. b) Test the null hypothesis. Give the test statistic and the p-value, and your conclusion. c) Give a 90% confidence interval for the difference in proportions

Answer #1

Population | n | Natural (X) | p^=X/n |

Rural (1) | 160 | 62 | 0.3875 |

Urban (2) | 250 | 86 | 0.344 |

A recent survey of households that put up Christmas trees polled
both rural and urban households. Of the 148 rural households, 72
were found to put up a natural tree (as opposed to an artificial
one) and of 270 urban households, 109 put up a natural tree. An
association of Christmas tree growers wants to test the claim that
a higher proportion of rural households prefer natural trees than
urban households.
(a) State the claim, the negation of the claim,...

Consider a survey of customers who bought a Christmas tree
during the holiday season. Respondents were classified as either
living in a rural area (population #1) or living in an urban area
(population #2). Each respondent was asked whether they purchased a
natural tree or an artificial tree. The population proportions in
this study are the proportion of persons who bought a natural tree
(“success”). (Assume, for this analysis, that the survey was
conducted by drawing an SRS from rural...

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