Answer
$X^2\gt X_α^2$: the null hypothesis is rejected.
There is sufficient evidence to conclude that the frequency distribution of the number of successes does not follow the theoretical probability distribution.
Work Step by Step
$H_0:$ the frequency distribution of the number of successes follows the theoretical probability distribution.
$H_1:$ the frequency distribution of the number of successes does not follow the theoretical probability distribution.
In MINITAB, enter the values of the probability distribution obtained in part (b) in C1: P(0), P(1), P(2), ..., P(10), P(11 or 12), where P(11 or 12) = P(11) + P(12) = 0.000045 + 0.000002 = 0.000047
In C2 enter the given frequencies in the table. Do not forget to add the frequencies for 11 and 12 in the last bin (4 + 0 = 4).
Select Stat -> Tables -> Chi-Square Goodness-of-Fit Test
Select "Observed counts" and enter C2
In "Test" select "Specific proportions" and enter C1
The results of the test will be given.
$X^2=41.1996$
Let's use the $α=0.05$ level of significance.
$k=12$. So, $d.f.=12-1=11$
$X_α^2=X_{0.05}^2=19.675$
(According to Table VII, for d.f. = 11 and area to the right of critical value = 0.05)
Since $X^2\gt X_α^2$, we reject the null hypothesis.
