In a test of the hypothesis
1 answer:
Answer:
Step-by-step explanation:
Given that
sample size =n= 50
x bar = sample mean = 10.8
s = sample std deviation = 3.3
Mean difference = 50-10 = 40
Std error of sample = std dev / sqrt n=
Since population std dev is not known, we have to use t test
Test statistic t = Mean diff/std error =
df = 39
p value = 0.0000
Since p < 0.09 our significance level, we reject our null hypothesis.
A. There is sufficient evidence to reject Upper H 0 for alpha greater than 0.09
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All three series converge, so the answer is D.
The common ratios for each sequence are (I) -1/9, (II) -1/10, and (III) -1/3.
Consider a geometric sequence with the first term <em>a</em> and common ratio |<em>r</em>| < 1. Then the <em>n</em>-th partial sum (the sum of the first <em>n</em> terms) of the sequence is
Multiply both sides by <em>r</em> :
Subtract the latter sum from the first, which eliminates all but the first and last terms:
Solve for :
Then as gets arbitrarily large, the term will converge to 0, leaving us with
So the given series converge to
(I) -243/(1 + 1/9) = -2187/10
(II) -1.1/(1 + 1/10) = -1
(III) 27/(1 + 1/3) = 18