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Answer: The required probability of having 6th girl is 0.5.
Step-by-step explanation: Given that boys and girls are equally likely.
We are to find the probability of a couple having a baby girl when their sixth child is born, given that the first five children were all girls.
Since the events of having a boy and a girl are independent of each other, so
the probability of having 6th girl dose not depend on the birth of the first five girls.
We know that there are only two possible cases (either a boy or girl will born).
So, sample space, S = {G, B} and the event E of having a girl is, E = {G}.
That is, n(S) = 2 and n(E) = 1.
Therefore, the probability of event E is given by
Thus, the required probability of having 6th girl is 0.5.
Answer:
Comparing the p value with a significance level for example we see that
so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can conclude that the true means are not significantly different.
Step-by-step explanation:
Data given and notation
represent the mean for A
represent the mean for B
represent the sample standard deviation for A
represent the sample standard deviation for B
sample size for the group A
sample size for the group B
Significance level provided
t would represent the statistic (variable of interest)
Concepts and formulas to use
We need to conduct a hypothesis in order to check if the means are equal or not, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
We don't have the population standard deviation's but we assume that the population deviation is equal for both populations, so we can apply a t test to compare means, and the statistic is given by:
(1)
Where represent the standard deviation pooled given by:
t-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.
With the info given we can replace in formula (1) like this:
P value
We need to find first the degrees of freedom given by:
Since is a two tailed test the p value would be:
Comparing the p value with a significance level for example we see that
so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can conclude that the true means are not significantly different.