This is an example of an arithmetic series: 6 + 8 + 10 + 12 + . . . + (4 + 2n) + . . .
1 answer:
True. A series is arithmetic if its terms come from an arithmetic sequence.
And a sequence is said to be arithmetic any of its two consecutive terms differ by a fixed difference, common to any consecutive pair.
As you can see, in this case, all terms differ by 2, so the sequence
is arithmetic, and thus the series
is arithmetic as well.
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Answer:
II. This finding is significant for a two-tailed test at .01.
III. This finding is significant for a one-tailed test at .01.
d. II and III only
Step-by-step explanation:
1) Data given and notation
represent the battery life sample mean
represent the population standard deviation
sample size
represent the value that we want to test
represent the significance level for the hypothesis test.
t would represent the statistic (variable of interest)
represent the p value for the test (variable of interest)
2) State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the mean battery life is equal to 18 or not for parta I and II:
Null hypothesis:
Alternative hypothesis:
And for part III we have a one tailed test with the following hypothesis:
Null hypothesis:
Alternative hypothesis:
Since we know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:
(1)
z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
3) Calculate the statistic
We can replace in formula (1) the info given like this:
4) P-value
First we need to calculate the degrees of freedom given by:
Since is a two tailed test for parts I and II, the p value would be:
And for part III since we have a one right tailed test the p value is:
5) Conclusion
I. This finding is significant for a two-tailed test at .05.
Since the . We reject the null hypothesis so we don't have a significant result. FALSE
II. This finding is significant for a two-tailed test at .01.
Since the . We FAIL to reject the null hypothesis so we have a significant result. TRUE.
III. This finding is significant for a one-tailed test at .01.
Since the . We FAIL to reject the null hypothesis so we have a significant result. TRUE.
So then the correct options is:
d. II and III only