A company that manufactures batteries used in electric cars is reporting that their newest model of battery has a mean lifetime, μ, of 20 years. To test the company's claim, a competitor has selected 39 of these batteries at random. The mean lifetime of the sample is 21.1 years. Suppose the population standard deviation of these lifetimes is known to be 4.1 years. Is there enough evidence to reject the claim that the mean lifetime of the newest model is 20 years? Perform a hypothesis test, using the 0.10 level of significance. (a) State the null hypothesis and the alternative hypothesis H₁. Ho #:0 H D
A company that manufactures batteries used in electric cars is reporting that their newest model of battery has a mean lifetime, μ, of 20 years. To test the company's claim, a competitor has selected 39 of these batteries at random. The mean lifetime of the sample is 21.1 years. Suppose the population standard deviation of these lifetimes is known to be 4.1 years. Is there enough evidence to reject the claim that the mean lifetime of the newest model is 20 years? Perform a hypothesis test, using the 0.10 level of significance. (a) State the null hypothesis and the alternative hypothesis H₁. Ho #:0 H D
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![(b) Perform a Z-test and find the p-value.
Here is some information to help you with your Z-test.
• The value of the test statistic is given by
• The p-value is two times the area under the curve to the right of the value of the test statistic.
Step 2: Enter the test
statistic.
(Round to 3 decimal
places.)
Step 3: Shade the area
represented by the p-
value.
Step 4: Enter the p-
value.
(Round to 3 decimal
places.)
0.3
0.2
0.1
(c) Based on your answer to part (b), choose what can be concluded, at the 0.10 level of significance, about the claim
made by the company.
Since the p-value is less than (or equal to) the level of significance, the null hypothesis is
rejected. So, there is enough evidence to reject the claim that the mean lifetime of the
newest model of battery is 20 years.
o Since the p-value is less than (or equal to) the level of significance, the null hypothesis is
not rejected. So, there is not enough evidence to reject the claim that the mean lifetime of
the newest model of battery is 20 years.
Since the p-value is greater than the level of significance, the null hypothesis is rejected.
So, there is enough evidence to reject the claim that the mean lifetime of the newest model
of battery is 20 years.
Since the p-value is greater than the level of significance, the null hypothesis is not
rejected. So, there is not enough evidence to reject the claim that the mean lifetime of the
newest model of battery is 20 years.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F33bf65d4-1388-49d2-8bed-4f9b21effc49%2F75f082ed-05dd-4f7e-9772-b38997d97ee0%2F5q0dwif_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(b) Perform a Z-test and find the p-value.
Here is some information to help you with your Z-test.
• The value of the test statistic is given by
• The p-value is two times the area under the curve to the right of the value of the test statistic.
Step 2: Enter the test
statistic.
(Round to 3 decimal
places.)
Step 3: Shade the area
represented by the p-
value.
Step 4: Enter the p-
value.
(Round to 3 decimal
places.)
0.3
0.2
0.1
(c) Based on your answer to part (b), choose what can be concluded, at the 0.10 level of significance, about the claim
made by the company.
Since the p-value is less than (or equal to) the level of significance, the null hypothesis is
rejected. So, there is enough evidence to reject the claim that the mean lifetime of the
newest model of battery is 20 years.
o Since the p-value is less than (or equal to) the level of significance, the null hypothesis is
not rejected. So, there is not enough evidence to reject the claim that the mean lifetime of
the newest model of battery is 20 years.
Since the p-value is greater than the level of significance, the null hypothesis is rejected.
So, there is enough evidence to reject the claim that the mean lifetime of the newest model
of battery is 20 years.
Since the p-value is greater than the level of significance, the null hypothesis is not
rejected. So, there is not enough evidence to reject the claim that the mean lifetime of the
newest model of battery is 20 years.
![A company that manufactures batteries used in electric cars is reporting that their newest model of battery has a mean
lifetime, μ, of 20 years. To test the company's claim, a competitor has selected 39 of these batteries at random. The mean
lifetime of the sample is 21.1 years. Suppose the population standard deviation of these lifetimes is known to be 4.1 years.
Is there enough evidence to reject the claim that the mean lifetime of the newest model is 20 years? Perform a hypothesis
test, using the 0.10 level of significance.
(a) State the null hypothesis H, and the alternative hypothesis H₁.
Ho
H₂O
(b) Perform a z-test and find the p-value.
Here is some information to help you with your Z-test.
Standard Normal
Distribution
Step 1: Select one-tailed
or two-tailed.
O One-tailed
○ Two-tailed
Step 2: Enter the test
statistic.
(Round to 3 decimal
places.)
Step 3: Shade the area
represented by the p-
value.
• The value of the test statistic is given by *-.
√
The p-value is two times the area under the curve to the right of the value of the test statistic.
0.3
0.2
H x
0.1
O<0 oso
0>0
020 0-0 0-0
X
G
X](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F33bf65d4-1388-49d2-8bed-4f9b21effc49%2F75f082ed-05dd-4f7e-9772-b38997d97ee0%2Fl4wpgpj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A company that manufactures batteries used in electric cars is reporting that their newest model of battery has a mean
lifetime, μ, of 20 years. To test the company's claim, a competitor has selected 39 of these batteries at random. The mean
lifetime of the sample is 21.1 years. Suppose the population standard deviation of these lifetimes is known to be 4.1 years.
Is there enough evidence to reject the claim that the mean lifetime of the newest model is 20 years? Perform a hypothesis
test, using the 0.10 level of significance.
(a) State the null hypothesis H, and the alternative hypothesis H₁.
Ho
H₂O
(b) Perform a z-test and find the p-value.
Here is some information to help you with your Z-test.
Standard Normal
Distribution
Step 1: Select one-tailed
or two-tailed.
O One-tailed
○ Two-tailed
Step 2: Enter the test
statistic.
(Round to 3 decimal
places.)
Step 3: Shade the area
represented by the p-
value.
• The value of the test statistic is given by *-.
√
The p-value is two times the area under the curve to the right of the value of the test statistic.
0.3
0.2
H x
0.1
O<0 oso
0>0
020 0-0 0-0
X
G
X
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