Conduct a 1 sample t-test to see if the mean LFPR in 1968 differed significantly
ID: 3135506 • Letter: C
Question
Conduct a 1 sample t-test to see if the mean LFPR in 1968 differed significantly from 0.5, using ?=0.05. Answer the following questions, and round to 4 decimal places.
a. The standard error of the sample mean is:
b. The test statistic is t =
c. The p-value is:
d. The statistical decision is which of the following:
Simultaneously reject and FTR Ho
Reject Ho
Accept Ho
FTR Ho
RoW City 1972 1968 diff (1972 0.03 0 N.Y 0.45 0.42 L.A Chicago Philadelphia Detroit San Francis Boston Pitt St. Louis Connecticut Wash., D.C. Cinn Baltimore Newark Minn/St. Pa Buffalo Houston Patterson Dallas 2 3 0.52 0.45 0.46 0.55 0.52 0.45 0.43 0.55 0.45 0.34 0.45 0.54 0.42 0.51 0.49 0.54 0 0.03 0 0.15 0.15 5 6 0.49 0.35 0.55 0.52 0.53 0.57 0.53 0.59 0.64 8 0.01 10 11 12 13 0.02 0.08 0.01 0.09 0.06 0.01 0.01 0.01 16 17 18 19 20 21 02 0.58 0.49 0.56 0.63 0.57 0.64Explanation / Answer
Formulating the null and alternative hypotheses,
Ho: u = 0.5
Ha: u =/ 0.5
As we can see, this is a two tailed test.
a)
Using technology,
s = standard deviation = 0.067991228
Hence, the standard error is
SE = s/sqrt(n) = 0.067991228/sqrt(19) = 0.015598257 [ANSWER]
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b)
Getting the test statistic, as
X = sample mean = 0.493157895
uo = hypothesized mean = 0.5
n = sample size = 19
s = standard deviation = 0.067991228
Thus, t = (X - uo) * sqrt(n) / s = -0.438645491 [ANSWER]
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c)
As
df = n - 1 = 18
Hence, the p value is, as this is two tailed,
p = 0.666137985 [ANSWER]
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d)
As P > 0.05, we FTR Ho. [ANSWER, OPTION D]
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