Hi!
<u>Given these two equations:</u>
We want to solve using the substitution method. Knowing that x is equal to y + 8, we can simply plug in 'y + 8' in for x in the second equation, like so:
Combine like terms on both sides:
Subtract y from both sides:
Subtract 8 from both sides:
Now, we can simply plug the y value in to the first equation, and solve for x:
Simplify:
<u>Learn more about the substitution (and also elimination!) method here:</u>
Answer:
The test statistic is z=2.5.
The null hypothesis is rejected.
There is enough evidence to support the claim that more than 10% of the 16 ounce cups are underfilled.
Step-by-step explanation:
This is a hypothesis test for a proportion.
The claim is that more than 10% of the 16 ounce cups are underfilled.
Then, the null and alternative hypothesis are:
The significance level is assumed to be 0.05.
The sample has a size n=100.
The sample proportion is p=0.18.
The standard error of the proportion is:
Then, we can calculate the z-statistic as:
This test is a right-tailed test, so the P-value for this test is calculated as:
As the P-value (0.006) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that more than 10% of the 16 ounce cups are underfilled.