The Batteries sheet of the Data Excel file 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.Perform a 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.Let:µLi-ion be the true average number of minutes per charge for Li-ion batteriesµNiMH be the true average number of minutes per charge for NiMH batteries. t-Test: Two-Sample Assuming Unequal Variances NiMHLi-ion Mean89.3571495 Variance3.9395659.75 Observations1417 Hypothesized Mean Difference0 df19 t Stat-2.89621 P(T<=t) one-tail0.004628 t Critical one-tail1.729133 P(T<=t) two-tail0.009255 t Critical two-tail2.093024 Based on the graph and the given information, why the two-sample t-test is valid for this study? (select all that are true). options: The sample data contain no outliers. The sample size is large enough (because n1+n2 = 14+17 = 31 is not more than 40). The sample data contain at least one outlier. Each population can reasonably be assumed to be normal because sampled data do not deviate much from a normal distribution. Each population cannot reasonably be assumed to be normal because samples do not have approximately a normal distributions. The samples are random and independent. The samples are not independent. The samples are not random. Select the correct answer for null and alternative hypotheses for this test. options: H0 : µNiMH - µLi-ion = 0 H1 : µNiMH - µLi-ion < 0 H0 : µNiMH - µLi-ion = 0 H1 : µNiMH - µLi-ion > 0 H0 : µNiMH - µLi-ion = 0 H1 : µNiMH - µLi-ion ≠ 0From the data given from the t Test: Two Sample Assuming Unequal Variances chart what would be the P value?Options:89.3570.00461.7290.00932.093 Based on your two-sample t-test output in the Excel file, select the conclusion at 5% significance level. options: p-value is larger than significance level. Do not reject H0There is insufficient evidence to conclude that true average number of minutes per charge for NiMH batteries is smaller than that for Li-ion batteries. p-value is larger than significance level. Do not reject H0There is insufficient evidence to conclude that true average number of minutes per charge for NiMH batteries is larger than that for Li-ion batteries. p-value is smaller than significance level. Reject H0There is sufficient evidence to conclude that true average number of minutes per charge for NiMH batteries is smaller than that for Li-ion batteries. p-value is smaller than significance level. Reject H0There is sufficient evidence to conclude that true average number of minutes per charge for NiMH batteries is larger than that for Li-ion batteries.

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Description: The Batteries sheet of the Data Excel file 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.Per

given that significance level (α) = 0.05

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The Batteries sheet of the Data Excel file 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.

Perform a 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.

Let:µ_Li-ion be the true average number of minutes per charge for Li-ion batteries

µ_NiMH be the true average number of minutes per charge for NiMH batteries.

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

Based on the graph and the given information, why the two-sample t-test is valid for this study? (select all that are true).

options:

	The sample data contain no outliers.
	The sample size is large enough (because n1+n2 = 14+17 = 31 is not more than 40).
	The sample data contain at least one outlier.
	Each population can reasonably be assumed to be normal because sampled data do not deviate much from a normal distribution.
	Each population cannot reasonably be assumed to be normal because samples do not have approximately a normal distributions.
	The samples are random and independent.
	The samples are not independent.
	The samples are not random.

Select the correct answer for null and alternative hypotheses for this test.

options:

	H₀ : µ_NiMH - µ_Li-ion = 0 H₁ : µ_NiMH - µ_Li-ion < 0
	H₀ : µ_NiMH - µ_Li-ion = 0 H₁ : µ_NiMH - µ_Li-ion > 0
	H₀ : µ_NiMH - µ_Li-ion = 0 H₁ : µ_NiMH - µ_Li-ion ≠ 0

From the data given from the t Test: Two Sample Assuming Unequal Variances chart what would be the P value?

Options:

89.357

0.0046

1.729

0.0093

2.093

Based on your two-sample t-test output in the Excel file, select the conclusion at 5% significance level.

options:

	p-value is larger than significance level. Do not reject H₀ There is insufficient evidence to conclude that true average number of minutes per charge for NiMH batteries is smaller than that for Li-ion batteries.
	p-value is larger than significance level. Do not reject H₀ There is insufficient evidence to conclude that true average number of minutes per charge for NiMH batteries is larger than that for Li-ion batteries.
	p-value is smaller than significance level. Reject H₀ There is sufficient evidence to conclude that true average number of minutes per charge for NiMH batteries is smaller than that for Li-ion batteries.
	p-value is smaller than significance level. Reject H₀ There is sufficient evidence to conclude that true average number of minutes per charge for NiMH batteries is larger than that for Li-ion batteries.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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