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 120 units of the leading product provides a mean battery life of 5 hours and 40 minutes with a standard deviation of 30 minutes. A similar analysis of 100 units of the new product results in a mean battery life of 8 hours and 5 minutes and a standard deviation of 55 minutes. It is not reasonable to assume that the population variances of the two products are equal. Use Table 2.

 

All times are converted into minutes. (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.

 

multiple choice 1

• 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.

 

multiple choice 2

• p-value < 0.01

• 0.01 ≤ p-value < 0.025

• 0.025 ≤ p-value < 0.05

• 0.05 ≤ p-value < 0.10

• p-value ≥ 0.10

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?

 

Answer 1