replied 2 years ago.
Hello here are my answers:
First situation. We want to know if there is a significant difference between the mean IQ test scores of 10,000 male and 10,000 female students. Although the two mean IQ tests are, by just looking, are not numerically equal, and we want to know if the difference is statistically significant. In order to determine this, we will conduct a statistical hypothesis testing. And once we computed the p value, and we got a small value, let us say 0.0001, which is way smaller than 0.05, then we can say that the difference is statistically significant, which means is not due by chance only. Therefore we can say that the two mean IQ tests are statistically significant. And we can attribute this difference , by the gender factor.
We want to know if there is a link between male breast cancer and obesity. We conduct a study and correlate, let us say 1000 males and computed a p value for correlation of about 0.002, This means that although the value of the correlation coefficient is not zero, and since our computed p-value is too small, smaller than the alpha value of 0.05, we can say that this result is statistically significant. We can attribute the difference is not due by chance or random error, like for example, sampling error.
We want to know If there is a connection between gender and voting preference among republican, democratic and independent candidates, and so we conduct a statistical hypothesis test using Chi square test of independence, and once we computed the p –value, let us say the value is 0.003, and since this p-value is smaller than the chosen alpha value, let us say, 0.05, then the result is statistically significant, and we can say that there is a relationship between gender and voting preference. Thus, gender play a factor on which candidates are being voted, based on their political affiliations.
All three situations resulted to statistically significant results.
Solving a problem using scientific method and solving a problem using statistical hypothesis testing, are somewhat similar in some steps, for example, we start with a problem, then we state our hypothesis, then we gather data, and analyze them and compute the results, and based on the result, we will draw our conclusions, whether our hypothesis is correct or not, and therefore, decide to accept it or reject it.
But there are also some differences, technically speaking, for example, in a scientific method, we test the hypothesis, by conducting experiments, gathering data and analyzing them, to get the result, while in statistical hypothesis testing, we test the hypothesis, by conducting statistical test, then comparing the critical and computed value or the p-value and the alpha value, in order to draw conclusion.
Oftentimes, statistical hypothesis tests are also used in a scientific method.
Some situations which we can say that it is practically significant, let us say, eating chocolates will make you overweight, but actually, using statistical hypothesis testing, this was proved a long time, that not all chocolates are actually causing one to become overweight, for example, study showed that eating dark chocolates, actually help to reduce hypertension and overweight.
Another situation, we can say that a coin is usually fair, or practically significantly fair, since we know there is an equal chance of getting a head and a tail once you toss it, but that assumption can be proved wrong if one conduct a statistical test, (using Z test for 2 sample proportions) and if your computed p-value is less than the chosen alpha value (let us say 0.05) then we can conclude that the coin is not fair, since the difference between the proportion of number of heads and tails are statistically significant.
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