The "lifetime" of a special battery can be described by a continuous random variable T, which is suspected to follow an exponential distribution with the
distribution function $F_0(t)=1-e^{-0.001t}$, where t is in hours (h) and t > 0. A sample survey with n = 99.0 randomly selected batteries from the
production series resulted in the following outcome (the n measured values of the lifetime T were divided into k = 6 classes with the specified frequencies
$n_i$
classes
30.0 24.0
0 < T < 400 400 < T < 800
16.0 9.0
7.0 13.0
800 < T < 1200 1200 < T < 1600 1600 < T < 2000 2000 < T
Use a $\chi^2$ test on the significance level $\alpha = 0.05$ to decide whether T has the distribution $F_0$. Calculate the test statistic and rejection region.
($H_0: F_T = F_0$, $H_1: F_T \neq F_0$)
test statistic: 0.75, rejection region: (11.07,∞)
test statistic: 0.65, rejection region: (10.97,∞)
test statistic: 0.75, rejection region: (10.97,∞)
test statistic: 0.65, rejection region: (11.07,∞)