The sequence is given to be:
The nth term of an arithmetic sequence is calculated using the formula:
where a₁ is the first term, n is the number of terms, and d is the common difference.
From the given sequence, the following parameters can be gotten:
Therefore, the parameters can be substituted into the formula to find the 52nd term:
The 52nd term is -438.
Answer:
P-value for this hypothesis test is 0.00175.
Step-by-step explanation:
We are given that the alumni association conducted a survey to see if alumni were in favor of firing the coach.
A simple random sample of 100 alumni from the population of all living alumni was taken. Sixty-four of the alumni in the sample were in favor of firing the coach.
<u><em>Let p = proportion of all living alumni who favored firing the coach</em></u>
SO, Null Hypothesis, : p = 0.50 {means that the majority of alumni are not in favor of firing the coach}
Alternate Hypothesis, : p > 0.50 {means that the majority of alumni are in favor of firing the coach}
The test statistics that will be used here is <u>One-sample z proportion</u> <u>statistics</u>;
T.S. = ~ N(0,1)
where, = sample proportion of the alumni in the sample who were in favor of firing the coach =
= 0.64
n = sample of alumni = 100
So, <em><u>test statistics</u></em> =
= 2.92
<u>Now, P-value of the hypothesis test is given by ;</u>
P-value = P(Z > 2.92) = 1 - P(Z 2.92)
= 1 - 0.99825 = 0.00175
Therefore, the P-value for this hypothesis test is 0.00175.