You suspect that people living in urban areas produce on average more garbage (X) than those living in rural areas (Y). To verify this opinion, you draw two samples and collect information on the amount of garbage produced in a month (measured in kilos). The first sample, made of 8 subjects living in an urban area, provides a sample mean equal to 40.5 and a sample standard deviation equal to 5.6; in the second sample, made of 10 subjects living in rural areas, the sample mean is 35.6 and the sample standard deviation is 7.5. It is assumed that the two populations are normal with the same unknown variance. Test the null hypothesis that the two population means are equal against a one-sided alternative according to which people living in urban areas produce on average more garbage than those living in rural areas. Use a 1% significance level.
You suspect that people living in urban areas produce on average more garbage (X)
than those living in rural areas (Y). To verify this opinion, you draw two samples and collect
information on the amount of garbage produced in a month (measured in kilos). The first sample,
made of 8 subjects living in an urban area, provides a sample
standard deviation equal to 5.6; in the second sample, made of 10 subjects living in rural areas, the
sample mean is 35.6 and the sample standard deviation is 7.5. It is assumed that the two populations
are normal with the same unknown variance.
Test the null hypothesis that the two population means are equal against a one-sided alternative
according to which people living in urban areas produce on average more garbage than those living
in rural areas. Use a 1% significance level.
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