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. 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?

Answer 1

$Null~hypothesis:~H_0:~\mu_1\leq \mu_2\\ Alternative~hypothesis:~H_1:\mu_1>\mu_2$

Two-Sample T-Test and CI

Sample N Mean StDev SE Mean
1 29 127.00 5.50 1.0
2 16 115.00 4.20 1.1

Difference = mu (1) - mu (2)
Estimate for difference: 12.00
95% lower bound for difference: 9.53
T-Test of difference = 0 (vs >): T-Value = 8.19 P-Value = 0.000 DF = 38

Since p-value<0.05 so we reject null hypothesis and conclude that the mean life for sub-compact cameras is greater than the mean life of compact cameras.