An investigator conducted a study to find the relationship between the number of

Question

An investigator conducted a study to find the relationship between the number of decayed, missing, or filled teeth (DMFT) and sugar consumption. The investigator produced an estimate for the correlation coefficient and provided the following statement: “The correlation between DMFT and sugar consumption is 0.7. There is a strong correlation between DMFT and sugar consumption. Therefore, it is recommended that patients be advised to reduce sugar consumption to prevent tooth decay.” State why you are or you are not confident about this investigator’s conclusion. In other words, explain if something is missing from this investigator’s analysis or if all you need is provided?

Explanation / Answer

Sol:

In cases such as these, we answer our research question concerning the existence of a linear relationship by using the t-test for testing the population correlation coefficient H0: = 0.

Let's jump right to it! We follow standard hypothesis test procedures in conducting a hypothesis test for the population correlation coefficient .

Null hypothesis H0: = 0
Alternative hypothesis HA: 0

Second, we calculate the value of the test statistic using the following formula:

Test statistic:

Third, we use the resulting test statistic to calculate the P-value. As always, the P-value is the answer to the question "how likely is it that we’d get a test statistic t* as extreme as we did if the null hypothesis were true?" The P-value is determined by referring to a t-distribution with n-2 degrees of freedom.

Finally, we make a decision:

here x--- sugar consumption

y---DMFT

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