Question

A phone manufacturer wants to compete in the touch screen phone market. Management understands that the leading product has a less than desirable battery life. They aim to compete with a new touch screen phone that is guaranteed to have a battery life more than two hours longer than the leading product. A recent sample of 139 units of the leading product provides a mean battery life of 5 hours and 31 minutes with a standard deviation of 32 minutes. A similar analysis of 121 units of the new product results in a mean battery life of 8 hours and 1 minutes and a standard deviation of 56 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: z table or t 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.

• H₀: μ₁ − μ₂ = 120; H_A: μ₁ − μ₂ ≠ 120

• H₀: μ₁ − μ₂ ≥ 120; H_A: μ₁ − μ₂ < 120

• H₀: μ₁ − μ₂ ≤ 120; H_A: μ₁ − μ₂ > 120

b-1. Calculate the value of the test statistic. (Round all intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)

b-2. Find the p-value.

• p-value < 0.01

• p-value 0.10
• 0.05 p-value < 0.10
• 0.025 p-value < 0.05
• 0.01 p-value < 0.025

b-3. At the 5% significance level, is the claim that the new product has, on 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.

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Answer 1