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Answer:
1. B. H0: μ1−μ2=0, HA: μ1−μ2≠0
2. z=1.2114
3. P-value=0.2257
4. Do not reject H0
Step-by-step explanation:
We have to perfomr an hypothesis test to see if there is strong evidence that there is a significant difference between the two population means.
The null and alternative hypothesis are:
Being μ1 the mean average gain for younger mothers and μ2 the mean average gain for mature mothers.
(NOTE: we are comparing means, not proportions, as it is the random variable is the weight gain).
As we are claiming "strong evidence", the level of significance will be 0.01.
For younger mothers, the sample size is n1=840, the sample mean is 30.7 and the sample standard deviation is s1=14.91.
For mature mothers, the sample size is n2=132, the sample mean is 29.15 and the sample standard deviation is s2=13.46.
The difference between means is
The standard error of the difference between means is
Then, the statistic can be calculated as:
The P-value for this z-statistic in a two tailed test is:
As the P-value is greater than the significance level, the null hypothesis failed to be rejected.
There is no enough evidence to claim that the real average weight gain differs from mature and youger mothers.
Answer:
.
Step-by-step explanation:
Let denote a constant (a number, rather than a variable like
.)
Let denote an expression about
(for example,
By the factor theorem, if is a factor of
, then
. In other words, if all mentions of
in the expression
are replaced with
, then the expression should evaluate to zero.
is equivalent to
. That is:
.
Replace all mentions of in
by
to get:
.
That should evaluate to zero. Therefore: . Solve for
to get
.