The following table shows the results of two random samples that measured the av
ID: 3221723 • Letter: T
Question
The following table shows the results of two random samples that measured the average number of minutes per charge for AA Lithium-ion (Li-ion) rechargeable batteries versus Nickel-Metal Hydride (NiMH) rechargeable batteries. Complete parts a through c.
Li-ion
NiMH
Sample mean
96.2
82.8
Sample standard deviation
6.3
11.3
Sample size
14
19
a. Perform a hypothesis test using
alphaequals=0.10
to determine if the average number of minutes per charge differs between these two battery types. Assume the population variances for the number of minutes per charge are not equal.
Determine the null and alternative hypotheses for the test.
Calculate the appropriate test statistic and interpret the result.
(Round to two decimal places as needed.)
The critical value(s) is(are)
(Round to two decimal places as needed. Use a comma to separate answers as needed.)
Because the test statistic
is greater than the critical value,
falls within the critical values,
is less than the critical value,
does not fall within the critical values,
do not reject
reject
the null hypothesis.
b. Identify the p-value from part a and interpret the result.
The p-value is
(Round to three decimal places as needed.)
Interpret the result. Choose the correct answer below.
A.
Since the p-value is
lessless
than the significance level,
do not rejectdo not reject
the null hypothesis.
B.
Since the p-value is
lessless
than the significance level,
rejectreject
the null hypothesis.
C.
Since the p-value is
not lessnot less
than the significance level,
do not rejectdo not reject
the null hypothesis.
D.
Since the p-value is
not lessnot less
than the significance level,
rejectreject
the null hypothesis.
c. What assumptions need to be made in order to perform this procedure?
A.
Although the sample size in the second sample is large enough, it must be assumed that the distribution for the first sample is normally distributed, and that the samples are independent.
B.
Although the sample size in the first sample is large enough, it must be assumed that the distribution for the second population is normally distributed, and that the samples are independent.
C.
It must be assumed that the distribution for both populations are normally distributed, and that the samples are independent.
D.
Since the sample sizes are large enough, no assumptions are needed
Li-ion
NiMH
Sample mean
96.2
82.8
Sample standard deviation
6.3
11.3
Sample size
14
19
Explanation / Answer
Below are the null and alternate hypothesis
p-value = 0.00069
As p-value is less than significance level of 0.10, we reject null hypothesis.
Critical Value is
Test statistics is greater than the critical value.
Null Hypothesis Alternate Hypothesis H0: 1 = 2 Ha: 1 2Related Questions
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