Question
In: Statistics and Probability
Let ? denote the life length, in hours, of a battery. Suppose ? is known to...
Let ? denote the life length, in hours, of a battery. Suppose ? is known to be normally distributed with standard deviation ? = 2.2 hours. A random sample of 16 batteries has an average life of ?̅ = 41.1 hours. We are interested in determining whether there is evidence to support the claim that mean battery life exceeds 40 hours. Using a level of significance of 0.05, answer the following questions.
a.) State the null and alternative hypothesis for the appropriate hypothesis test
b.)Identify the test statistic and critical region. State the conclusion of the test (i.e., should we reject or fail to reject).
c.) What is the ?-value for this test? Using this ?-value, what would be the conclusion of our test if the level of significance was changed to 0.025?
d.) What is the Type II error probability for the test if the true mean life is 41.496 hours? If the true mean life is 41.496 hours, what is the power of the test?
Solutions
orchestra answered 2 years agoRelated Solutions
True or False: The life in hours of a battery is known to be approximately normally...
True or False: The life in hours of a battery
is known to be approximately normally distributed, with standard
deviation of 15 hours. A random sample of 16 batteries has a mean
life of 110 hours. Based on sampling results, there is sufficient
evidence on this sample to support the claim that battery life
exceeds 100 hours at α=0.05.
1)The life in hours of a battery is known to be approximately normally distributed, with standard...
1)The life in hours of a battery is known to be approximately
normally distributed, with standard deviation 1.25 hours. A random
sample of 10 batteries has a mean life of 40.5 hours. A. Is there
evidence to support the claim that battery life exceeds 40 hours ?
Use α= 0.05.
B. What is the P-value for the test in part A?
C. What is the β-error for the test in part A if the true mean
life is 42 hours?...
Suppose that the length of life (in hours) of an item in the machine shop has...
Suppose that the length of life (in hours) of an item in the
machine shop has a Weibull distribution with α = 0.01 and β =
2.
(a) What is the probability that it lasts longer than 10 hours
of usage?
(b) Find the median and the first quartile of the life of this
item.
(c) How long is such an item expected to last? Use the fact that
Γ(1.5) = 0.8862
Suppose that the length of life (in hours) of an item in the machine shop has...
Suppose that the length of life (in hours) of an item in
the machine shop has a Weibull distribution with α = 0.01 and β =
2.
(a) What is the probability that it lasts longer than 10
hours of usage?
(b) Find the median and the first quartile of the life
of this item.
(c) How long is such an item expected to last? Use the
fact that Γ(1.5) = 0.8862.
Suppose that for a specic model of cell phone, the life-length of a fully-charged cellphone battery...
Suppose that for a specic model of cell phone, the life-length
of a fully-charged cellphone battery is normally distributed with a
mean of 1200 minutes and a standard deviation of 160 minutes.
(a) A person charges his/her cellphone at night and uses it
during the day for about 16 hours. What is the probability that
he/she does not have to charge his/her cell phone during the
day?
(b) 80% of fully-charged cell-phone batteries have a life-length
more than how many...
An important feature of tablets is battery life, the number of hours before the battery needs...
An important feature of tablets is battery life, the number of
hours before the battery needs to be recharged. The data shown in
the table below contain the battery life of 10 WiFi-only and 10
3G/4G/WiFi 9- through 12-inch tablets. Complete parts (a)
through (c).
WiFi-only
3G/4G/WiFi
4444
2525
3030
3535
4242
7070
5050
5454
5050
5555
5050
2121
3535
5959
5555
2525
3535
3232
4141
6666
a. Assuming that the population variances from both types of
tablets are equal,...
An important feature of tablets is battery life, the number of hours before the battery needs...
An important feature of tablets is battery life, the number of
hours before the battery needs to be recharged. The following table
shows the battery life of 12 WiFi-only and 7 3G/4G/WiFi 9-through
12-inch tablets:
WiFi Only
3G/4G+WiFi
12.40
11.70
10.60
11.40
11.50
10.70
12.60
11.50
8.00
11.30
10.90
11.60
11.60
8.90
10.00
10.90
8.90
9.50
10.50
Assuming that the population variances from both types of
tablets are equal, is there evidence of a difference in the means
battery life...
An important feature of tablets is battery life, the number of hours before the battery needs...
An important feature of tablets is battery life, the number of
hours before the battery needs to be recharged. The file Tablets
contains the battery life of 12 WiFi-only and 7 3G/4G/WiFi 9-
through 12-inch tablets. (Data extracted from “Ratings and rec-
ommendations: Tablets,” Consumer Reports, August 2013, p.
24.)
a. Assuming that the population variances from both types
of
tablets are equal, is there evidence of a difference in the
mean
battery life between the two types of tablets?...
An important feature of tablets is battery life, the number of hours before the battery needs...
An important feature of tablets is battery life, the number of
hours before the battery needs to be recharged. The data shown in
the table below contain the battery life of 10 WiFi-only and 10
3G/4G/WiFi 9- through 12-inch tablets.
WiFi-only
3G/4G/WiFi
48
26
35
40
44
65
52
51
60
52
48
23
38
51
56
25
36
31
50
66
a. Assuming that the population variances from both types of
tablets are equal, is there evidence of a...
Let the random variable X denote the time (hours) for which a part is waiting for...
Let the random variable X denote the time (hours) for which a
part is waiting for the beginning of the inspection process since
its arrival at the inspection station, and let Y denote the time
(hours) until the inspection process is completed since its arrival
at the inspection station. Since both X and Y measure the time
since the arrival of the part at the inspection station, always X
< Y is true. The joint probability density function for X...
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