STAT177 Homework sheet #7 Solutions
1)
Both sample sizes are
at least 30 and the number of successes/failures is at least 5 for both
samples. Thus, the Z test is the appropriate test.
2)
We choose members as
group 1. Here is the output:
|
Z test
for two proportions |
|
Ho:
proportion 1 - proportion 2 is not greater than 0 |
|
Ha:
proportion 1 - proportion 2 is greater than 0 |
|
Reject Ho
if test statistic > 1.645 |
|
Test
statistic = 3.035 |
|
P-value =
0.001 |
|
Reject Ho |
|
Conclude
proportion 1 - proportion 2 is greater than 0 |
|
95%
confidence interval of proportion 1 - proportion 2: 0.052 to 0.238 |
Since the p-value of 0.001 is less than the level of
significance, we reject Ho and conclude that members are more likely to visit new
exhibits.
3)
Under the general rule
of thumb, the p-value provides strong support for Ha since it is less than 1%.
There is no level of significance between 1% and 10% in which the opposite
conclusion would be reached.
4) Here is the output:
|
Chi-square
test for independence |
|
Ho: the
variables are independent |
|
Ha: the
variables are not independent |
|
Reject Ho
if test statistic > 9.488 |
|
Test
statistic = 13.623 |
|
P-value =
0.009 |
|
Reject Ho |
|
Conclude
the variables are not independent |
|
Degree of
dependence: 15.07% |
Since the p-value is less than the level of significance, we reject Ho and conclude the sales depend on the counter. We see that the amount of the sale depends on which counter it is from 15.07% of the time.
5) Since there are 100 sales for each counter, there is no need to reweigh the percentages for each counter. Here is the histogram:
