Please no written by hand solutions A promising start-up wants to compete in the cell phone market. The start-up believes that the battery life of its cell phone is more than two hours longer than the leading product. A recent sample of 120 units of the leading product provides a mean battery life of 6 hours and 30 minutes with a standard deviation of 25 minutes. A similar analysis of 129 units of the start-up's product results in a mean battery life of 8 hours and 47 minutes and a standard deviation of 29 minutes. It is not reasonable to assume that the population variances of the two products are equal. All times are converted into minutes. Let new products and leading products represent population 1 and population 2, respectively. (You may find it useful to reference the appropriate table: table or table) a. Set up the hypotheses to test if the new product has a battery life more than two hours longer than the leading product. Но: Н1 - Н2 = 120; Нд: 1 - H2 # 120 • HO: M1 - 12 2 120: HA: M1 - H2 < 120 • HO: M1 - H2 5 120; HA: H1 - H2 > 120 b-1. Calculate the value of the test statistic. (Round final answer to 3 decimal places.) b-2. Find the p-value. • p-value < 0.01 O pivalue › 0.10 O 0.05 s p-value < 010 O 0.025 s p-value < 0.05 O 0.01 s pvalue < 0.025 b-3. At the 5% significance level, is the claim that the new product has n average, a battery life of more than two hours longer than the leading product is supported by the sample data? __ H0. The claim that the new product has, on average, a battery life of more than two hours longer than the leading product is _ by the sample data at the 5% significance level.

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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A promising start-up wants to compete in the cell phone market. The start-up believes that the battery life of its cell phone is more than two hours longer than the leading product. A recent sample of 120 units of the leading product provides a mean battery life of 6 hours and 30 minutes with a standard deviation of 25 minutes. A similar analysis of 129 units of the start-up's product results in a mean battery life of 8 hours and 47 minutes and a standard deviation of 29 minutes. It is not reasonable to assume that the population variances of the two products are equal.

All times are converted into minutes. Let new products and leading products represent population 1 and population 2, respectively.

(You may find it useful to reference the appropriate table: table or table)

a. Set up the hypotheses to test if the new product has a battery life more than two hours longer than the leading product.

Но: Н1 - Н2 = 120; Нд: 1 - H2 # 120

• HO: M1 - 12 2 120: HA: M1 - H2 < 120

• HO: M1 - H2 5 120; HA: H1 - H2 > 120

b-1. Calculate the value of the test statistic. (Round final answer to 3 decimal places.)

b-2. Find the p-value.

• p-value < 0.01

O pivalue › 0.10

O 0.05 s p-value < 010

O 0.025 s p-value < 0.05

O 0.01 s pvalue < 0.025

b-3. At the 5% significance level, is the claim that the new product has n average, a battery life of more than two hours longer than the leading product is supported by the sample data?

______ H0. The claim that the new product has, on average, a battery life of more than two hours longer than the leading product is _____ by the sample data at the 5% significance level.

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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