By Dr Mussa Abdulkadir
1. Interpretation
We are 90% confident that the mean price all summer sleeping bags that keep you warm from
200 𝐹 𝑡𝑜 450 𝐹 is found between $72.55 and $94.95.
2.
a) We test 𝐻0 : μ = 67 cm vs. 𝐻𝑎 : μ ≠ 67 cm.
b) t = (61.8−67)/(10.6/√16).=−1.962.
c) The P-value is approximately equal to 0.069. This means that if the mean slab thickness in
the Vail region is the same as that of Canada, the probability that the sample mean will
take a value of 61.8 cm or less, or 72.2 cm or more is about 7%.
d) The P-value is greater than the given level of significance 𝛼 = 0.01. Hence, it is likely to
obtain a value of the sample mean of 61.8 cm when the mean slab thickness in the Vail
region is the same as that of Canada. Therefore, the sample data does not give sufficient
evidence supporting the mean slab thickness in the Vail region is different from that of
Canada.
3.
a) We test 𝐻0 : μ = 1.75 years vs. 𝐻𝑎 : μ > 1.75 𝑦𝑒𝑎𝑟𝑠
b) t = (2.05−1.75)/(0.82/√46).=2.481.
c) The P-value is approximately equal to 0.0084. This means that if the coyotes of this
region live 1.75 years on average, then the probability that the sample mean will take
a value of 2.05 years or more is about 0.8%.
d) The P-value is less than the given level of significance 𝛼 = 0.01. Hence, it is unlikely
to obtain a value of the sample mean of 2.05 years when the coyotes of this region live
1.75 years on average. Therefore, the sample data give sufficient evidence that
supports coyotes in this region of northern Minnesota tend to live longer than the
average of 1.75 years.
4.
a) We test 𝐻0 : μ = 4.8 millions s vs. 𝐻𝑎 : μ < 4.8 𝑚𝑖𝑙𝑙𝑖𝑜𝑛𝑠
b) t = (4.40−4.8)/(0.28/√6).=−3.499.
c) The P-value is approximately equal to 0.0086. This means that if the populations
mean RBC count for this patient is 4.8 millions, then the probability that the sample
mean will take a value of 4.40 million or less is about 0.9%.
d) The P-value is less than the given level of significance 𝛼 = 0.05. Hence, it is
unlikely to obtain a value of the sample mean of 4.40 million if the population
mean RBC count for this patient is 4.8 millions. Therefore, the given data indicates
that the population mean RBC count for this patient is lower than 4.8 millions.
5.
a) We test 𝐻0 : μ = 14 grams s vs. 𝐻𝑎 : μ > 14 𝑔𝑟𝑎𝑚𝑠
b) t = (15.1−14)/(2.51/√10).=−31.386.
c) The P-value is approximately equal to 0.09958. This means that if the populations
average HC for this patient is 14 grams, then the probability that the sample mean
will take a value of 15.1 grams or more is about 10%.
d) The P-value is greater than the given level of significance 𝛼 = 0.01. Hence, it is likely
to obtain a value of the sample mean of 15.1 grams if the population average HC for
this patient is 14 grams. Therefore, the given information does not indicate that the
populations average HC for this patient is higher than 14 grams.
6.
a) We test 𝐻0 : 𝜇𝑑 = 0 s vs. 𝐻𝑎 : 𝜇𝑑 ≠ 0.
b) t = (0.37−0)/(0.47/√7).=2.08.
c) The P-value is approximately equal to 0.00823. This means that if there is no
difference in the population mean hours per fish caught using a bout compared with
from the shore, then the probability that the difference of the sample means will take
a value −0.37 or less, or 0.37 or more is about 0.8%.
d) The P-value is less than the given level of significance 𝛼 = 0.01. Hence, it is unlikely
to obtain a value of the difference of the sample means of 0.37 if there is no
difference in the population mean hours per fish caught using a bout compared with
from the shore. Therefore, the given data indicate that that supports there is a
difference in the population mean hours per fish caught using a bout compared with
from the shore.
7.
a) We test 𝐻0 : 𝜇𝑑 = 0 s vs. 𝐻𝑎 : 𝜇𝑑 > 0.
b) t = (12.6−0)/(22.66/√5).=1.24.
c) The P-value is approximately equal to 0.14078. This means that if the pick wind gust in
January is the same as that of April on average, then the probability that the difference
of the sample means will take a value −12.60 or less, or 12.60 or more is about 14.1%.
d) The P-value is greater than the given level of significance 𝛼 = 0.01. Hence, it is likely
to obtain a value of the difference of the sample means of 12.60 if the pick wind gust in
January is the same as that of April on average. Therefore, the given sample
information does not support that the pick wind gusts are higher in January than in
April.