Answer:
i:
The appropriate null hypothesis is
The appropriate alternative hypothesis is
The p-value of the test is 0.1057 > 0.05, which means that there is not sufficient evidence that fewer than 20% of the museum visitors make use of the device, and so, it should not be withdrawn.
ii:
The p-value of the test is 0.1057
Step-by-step explanation:
Question i:
The device will be withdrawn if fewer than 20% of all of the museum’s visitors make use of it.
At the null hypothesis, we test if the proportion is of at least 20%, that is:
At the alternative hypothesis, we test if the proportion is less than 20%, that is:
The test statistic is:
In which X is the sample mean, is the value tested at the null hypothesis,
is the standard deviation and n is the size of the sample.
0.2 is tested at the null hypothesis:
This means that .
The device will be withdrawn if fewer than 20% of all of the museum’s visitors make use of it. Of a random sample of 100 visitors, 15 chose to use the device.
This means that
Test statistic:
P-value of the test and decision:
The p-value of the test is the probability of finding a sample proportion below 0.15, which is the p-value of z = -1.25.
Looking at the z-table, z = -1.25 has a p-value of 0.1057.
The p-value of the test is 0.1057 > 0.05, which means that there is not sufficient evidence that fewer than 20% of the museum visitors make use of the device, and so, it should not be withdrawn.
Question ii:
The p-value of the test is 0.1057