Question

Digital cameras have taken over the majority of the point-and-shoot camera market. One of the important features of a camera is the battery life, as measured by the number of shots taken until the battery needs to be recharged. A random sample of 29 sub-compact cameras (Population 1) yielded a mean of 127 shots between recharges, with a standard deviation of 5.5 shots. A random sample of 16 compact cameras (Population 2) yielded a mean of 115 shots between recharges, with a standard deviation of 4.2 shots. Assume that the population variances are not equal.

A) Using a significance level of α = .01, if a hypothesis is conducted to determine whether the mean battery life for sub-compact cameras is greater than the mean life of compact cameras, what conclusion should be reached?

1)There mean battery life for compact cameras is greater than the mean battery life of sub-compact cameras.

2)The mean battery life for sub-compact cameras is greater than the mean battery life of compact cameras,

3)The mean battery life for sub-compact cameras is not greater than the mean battery life of compact cameras,

4)There is no difference in the mean battery life for sub-compact and compact cameras.

B) What is the appropriate null hypothesis for determining whether the mean battery life for sub-compact cameras is greater than the mean life of compact cameras?

H₀: μ₁ < μ₂

H₀: μ₁ > μ₂

H₀: μ₁ ≥ μ₂

H₀: μ₁ ≤ μ₂

H₀: μ₁ = μ₂

H₀: μ₁ ≠ μ₂

C) Using only the statistical table in your textbook, what is the p-value of the most appropriate hypothesis test?

p = .0446

p > .10

p is between .025 and .05

p = .0892

p < .025

p is between .05 and .10

Answer 1

The statistical software output for this problem is:

Hence,

a) Conclusion: The mean battery life for sub-compact cameras is greater than the mean battery life of compact cameras.

Option 2 is correct.

b) Null: H₀: μ₁ ≤ μ₂; Option D is correct.

c) p < .025