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ramirezmarco1593
12.12.2019 •
Mathematics
Aprofessor of women's studies is interested in determining if stress affects the menstrual cycle. ten women are randomly sampled for an experiment and randomly divided into two groups. one of the groups is subjected to high stress for two months while the other lives in a relatively stress-free environment. the professor measures the menstrual cycle (in days) of each woman during the second month. the following data are obtained.
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Ответ:
Null hypothesis:![\mu_1 = \mu_2](/tpl/images/0415/7789/42a83.png)
Alternative hypothesis:![\mu_1 \neq \mu_2](/tpl/images/0415/7789/bc365.png)
Reject H0: stress affects the menstrual cycle
Step-by-step explanation:
The statistic is given by the following formula:
Where t follows a t distribution with
degrees of freedom
The system of hypothesis on this case are:
Null hypothesis:![\mu_1 = \mu_2](/tpl/images/0415/7789/42a83.png)
Alternative hypothesis:![\mu_1 \neq \mu_2](/tpl/images/0415/7789/bc365.png)
Or equivalently:
Null hypothesis:![\mu_1 - \mu_2 = 0](/tpl/images/0415/7789/16d3f.png)
Alternative hypothesis:![\mu_1 -\mu_2 \neq 0](/tpl/images/0415/7789/204ad.png)
Our notation on this case :
Tha data given is:
Group 1 (High stress) : 20,23,18,19,22
Group 2 (Relatively stress free): 26,31,25,26,30
We can calculate the sample mean and the sample deviation with the following formulas:
And now we can calculate the statistic:
Now we can calculate the degrees of freedom given by:
Now we can calculate the critical value since the confidence is 95% the value for the significance would be
and the value for
and if we find a critical value on th t distribution with 8 degrees of freedom that accumulates 0.025 of the area on each tail we got ![t_{crit}=\pm 2.306](/tpl/images/0415/7789/ac683.png)
Since our calculated value is lower than the critical value, we have enough evidence to reject the null hypothesis. And makes sense say that the difference between the two means are different at 5% of significance.
Reject H0: stress affects the menstrual cycle
Ответ:
7v +1
Step-by-step explanation:
6v+v+1
Combine like terms
7v +1