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GrogVix [38]
2 years ago
6

A study was conducted on the effects of long-term marriage (more than 10 years). Researchers gathered data from a random sample

of 4,563 adults and measured quite a few variables, in addition to the explanatory variable of marriage and the response variable of longer life span. According to a newspaper article summarizing the study, those in long-term marriages were more likely to be more physically active, at a healthy weight, and nonsmokers. Those who were not married were about 20% more likely to be deceased. What conclusion can we draw from this study? Explain.
We can infer a cause-and-effect relationship because the sample was selected randomly.

We cannot infer a cause-and-effect relationship because treatments were not assigned randomly.

We cannot infer a cause-and-effect relationship because we do not have a control group.

We can infer a cause-and-effect relationship because multiple variables were included.

We cannot infer a cause-and-effect relationship because the treatments imposed were not blocked correctly.
Mathematics
1 answer:
True [87]2 years ago
8 0

Answer:

The correct option is;

We cannot infer a cause and effect relationship because the multiple variables were included

Step-by-step explanation:

The criteria required in order to establish a cause and effect relationship includes the following;

1) There must be a temporal precedence between the cause and the effect such that the cause must take place before the effect

In the question, it is not clearly stated weather there was a divorce (the likely cause) takes place before the event

2) In the vent that the cause occurs, the effect must occur

Therefore, all those who are not married are expected to be deceased for there to be a cause and effect relationship

3) The cause and effect relationship must not be explicable by other factors

In the question, it is stated that those who were married were more likely to be active physically, maintain an healthy weight and were nonsmokers, which are factors that contribute to longevity.

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Is plausible that the successive throws are independent

Step-by-step explanation:

1) Table with info given

The observed values are given by the following table

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First shot          Made          Second shot missed           Total

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Made                  152                       33                                185

Missed                37                         8                                  45

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Total                    189                       41                                230

2) Calculations and test

We are interested on check independence and for this we need to conduct a chi square test, the next step would be find the expected value:

Null hypothesis: Independence between two successive free throws

Alternative hypothesis: No Independence between two successive free throws

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First shot                    Made                                    Second shot missed

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Made                  189(185)/230=152.0217                41(185)/230=32.9783

Missed                189(45)/230=36.9783                  41(45)/230=8.0217

_____________________________________________________

On this case all the expected values are higher than 5 and the sample size 230 is enough to apply the chi squared test.

3) Calculate the chi square statistic

The statistic for this case is given by:

\chi_{cal}^2 =\sum \frac{(O_i -E_i)}{E_i}

Where O represent the observed values and E the expected values. Replacing the values that we got we have this

\chi_{cal}^2 =\frac{(152-152.0217)^2}{152.0217}+\frac{(33-32.9783)^2}{32.9783}+\frac{(37-36.9783)^2}{36.9783}+\frac{(8-8.0217)^2}{8.0217}=0.000003098+0.00001428+0.00001273+0.0.00005870=0.00008881

Now with the calculated value we can find the degrees of freedom

df=(r-1)(c-1)=(2-1)(2-1)=1 on this case r means the number of rows and c the number of columns.

Now we can calculate the p value

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