Ho: There is no association between gender and newspaper
reading
Ha: There is an association between gender and newspaper
reading
test statistic: 8.261, p-value = .041
We would reject the null hypothesis at the .05 level and conclude there
is a relationship between gender and newspaper reading. (We would not reject
at the .01 level.)
(b)
The shaded region represents the probability of
seeing a test statistic as large as the one observed (8.261) when there
is no association. Since this probability is small (less than .05)
we make conclude that there probably is some association between gender
and newspaper reading..
(c) The cell that corresponds to the male, reading less than once
per week contributes the most to the test statistic. The observed count
is lower than the expected count for that cell, meaning that there are
fewer males reading less than once per week than we would’ve expected if
there was no relationship.
(d) The next three cells are the cells that correspond to men reading
every day, women reading every day, and women reading less than once per
week. There are more men than we would have expected reading every
day, there are fewer women then we would expected reading every day and
more women
than expected reading less than once per week. Seems men read more
than women.
Ho: There is no association between gender and suitability
opinion
Ha: There is an association between gender and suitability
opinion
test statistic: .01776, p-value: .89
With our large p-value, there is no evidence of an association between
gender and their opinion on whether men are more suitable for politics
than women.
(b) Let q1=proportion
of men who agree with the statement and q2=proportion
of women who agree with the statement
Ho: q1=q2
(men
and women agree in equal proportions)
Ha: q1¹q2(the
proportions of men and women who agree differs)
test statistic: -.13, p-value: .894
Again, with this large p-value, we would fail to reject Ho:
q1=q2,
giving
us no evidence that men and women don't agree in the same proportion.
(c) The p-values are equal, and
the conclusion is the same.
(d) z=-.13, z2=.0169
which is close to .018.
liberal | moderate | conservative | total | |
too little | 45 | 43 | 45 | 133 |
just right | 169 | 224 | 197 | 590 |
too much | 162 | 168 | 182 | 512 |
total | 376 | 435 | 424 | 1235 |
Chi-square statistic for this table: 4.174
(c) This is
smaller than 6.724, the chi-square statistic from the actual sample data.
(d)
(e) There were
11 values in this graph larger than 6.725. This is 11% of the repetitions.
(f) Earlier
we found p-value to be between .1 and .2, and .11 is within this range,
so yes, we are reasonable close. They should match since the p-value
tells us how often we expect to get a chi-square value at least this extreme
when the null hypothesis is true.