Help me please, NO links11th grade work
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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.
Consider the lengths of consecutive 1-2 blocks.
block 1 - 1, 2 - length 2
block 2 - 1, 2, 2 - length 3
block 3 - 1, 2, 2, 2 - length 4
block 4 - 1, 2, 2, 2, 2 - length 5
and so on.
Recall the formula for the sum of consecutive positive integers,
Now,
which means that the 1234th term in the sequence occurs somewhere about 1/5 of the way through the 49th 1-2 block.
In the first 48 blocks, the sequence contains 48 copies of 1 and 1 + 2 + 3 + ... + 47 copies of 2, hence they make up a total of
numbers, and their sum is
This leaves us with the contribution of the first 10 terms in the 49th block, which consist of one 1 and nine 2s with a sum of .
So, the sum of the first 1234 terms in the sequence is 2419.