Question

Digital cameras make up most of the? point-and-shoot camera market. One of the important features of a camera is battery life. In a sample of 31? sub-compact cameras and 15 compact? cameras, the mean and standard deviations? (respectively) are 240.65 and 114.22 shots? (subcompact) and 270 and 112.06 shots? (compact). Assume that the population variances are equal across the samples.?? a. If you want to test whether the battery lives differ across the camera? types, what is the correct set of? hypotheses? ?Hi:??mu1greater than mu2 ???? Ha:??mu1less than or equals??mu2 ?Ho: mu1 greater than or equalsmu2 ???Ha??mu1less than??mu2 ?Ho: mu1equalsmu2 ???? Ha:??mu1not equalsmu2 b. What is the test? statistic? 2.015 .8220 ?-.8220 c. What is the critical? value? ?-2.015 2.015 .8220 d. Basec on sample? evidence, what is correct? conclusion? Reject Ho. It appears that the battery lives differ. Reject Ho. It appears that the compact battery lasts longer. ?Don't reject Ho. It appears that the battery lives are the same.

Answer 1

H₀:

H_a:

The pooled variance(s_p²) = (n1 - 1)s1^2 + (n2 - 1)s2^2)/(n1 + n2 - 2)

                                         = (30 * (114.22)^2 + 14 * (112.06)^2)/(31 + 15 - 2)

                                          = 12890.69

The test statistic t = ()/sqrt(s_p²/n1 + s_p²/n2)

                            = (240 .65 - 270)/sqrt(12890.69/31 + 12890.69/15)

                           = -0.8220

DF = 31 + 15 - 2 = 44

With 44 df and 0.05 significance level the critical values are t_{0.025, 44} = +/- 2.015

As the test statistic value is not less than the critical value (-0.8220 > -2.015), so the null hypothesis is not rejected.

Don't reject H₀. It appears that the battery lives are the same.