This chart 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. Down below shows the hypothesis test using significance level (α) = 0.05 to determine if the true average number of minutes per charge for NiMH batteries is smaller than that for Li-ion batteries. 1. From the data given from the first graph below, what would be the correct p value? (the one tail or the two tail?) t-Test: Two-Sample Assuming Unequal Variances NiMH Li-ion Mean 89.35714 95 Variance 3.93956 59.75 Observations 14 17 Hypothesized Mean Difference 0 df 19 t Stat -2.89621 P(T<=t) one-tail 0.004628 t Critical one-tail 1.729133 P(T<=t) two-tail 0.009255 t Critical two-tail 2.093024 For the bottom graph: 1.. Find the point estimate (you can do this by subtracting Group 2 Sample Mean from Group 1 Sample Mean.) 2. Find the Lower Bound of the confidence interval by subtracting the Margin of Error from the point estimate. 3. Find the Upper Bound by adding the margin of error to the point estimate. Comparing Two Means When Variances Are NOT equal Group 1 Sample Mean: 89.35714 Group 1 Sample Standard Deviation: 3.93956 = SQRT(Variance) Group 1 Sample Size: 14 Group 2 Sample Mean: 95 Group 2 Sample Standard Deviation: 59.75 = SQRT(Variance) Group 2 Sample Size: 17 Alpha: 0.05 =1-Conf level Hypothesized Mean Difference: 0 This usually is zero Degrees of Freedom: 16.16881 Standard Error (SE) 14.52970 Test Statistic: -0.38837 P(T<=t) one-tail 0.35143 P(T<=t) two-tail 0.70286 Margin of Error (ME) 30.80159

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Description: This chart 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. Down below shows the hypothesis te

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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This chart 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. Down below shows the hypothesis test using significance level (α) = 0.05 to determine if the true average number of minutes per charge for NiMH batteries is smaller than that for Li-ion batteries.

1. From the data given from the first graph below, what would be the correct p value? (the one tail or the two tail?)

t-Test: Two-Sample Assuming Unequal Variances

	NiMH	Li-ion
Mean	89.35714	95
Variance	3.93956	59.75
Observations	14	17
Hypothesized Mean Difference	0
df	19
t Stat	-2.89621
P(T<=t) one-tail	0.004628
t Critical one-tail	1.729133
P(T<=t) two-tail	0.009255
t Critical two-tail	2.093024

For the bottom graph:

1.. Find the point estimate (you can do this by subtracting Group 2 Sample Mean from Group 1 Sample Mean.)

2. Find the Lower Bound of the confidence interval by subtracting the Margin of Error from the point estimate.

3. Find the Upper Bound by adding the margin of error to the point estimate.

Comparing Two Means When Variances Are NOT equal

Group 1 Sample Mean:	89.35714
Group 1 Sample Standard Deviation:	3.93956	= SQRT(Variance)
Group 1 Sample Size:	14
Group 2 Sample Mean:	95
Group 2 Sample Standard Deviation:	59.75	= SQRT(Variance)
Group 2 Sample Size:	17
Alpha:	0.05	=1-Conf level
Hypothesized Mean Difference:	0	This usually is zero

Degrees of Freedom:	16.16881
Standard Error (SE)	14.52970
Test Statistic:	-0.38837
P(T<=t) one-tail	0.35143
P(T<=t) two-tail	0.70286
Margin of Error (ME)	30.80159

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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