Question

Which code will find the 90 th percentile of the t-distribution with 10 degrees of freedom? Recall, that 90% percentile is the value a such that P(X≤a)=0.9 Hint: You may verify the answer by hand by checking the tistribution table in Quercus.

1. pt (0.9,10, lower.tail = FALSE )
2. qt (0.9,10)
3. pt(0.9,10)
4. qt(0.9,10, lower.tail = FALSE)

Answer 1

The code to find the 90th percentile of the t-distribution with 10 degrees of freedom is 'qt(0.9,10)'. This function provides the value below which 90% of the t-distribution is found which corresponds to the 90th percentile.

Step-by-step explanation:

To find the 90th percentile of the t-distribution with 10 degrees of freedom, you want to determine the score below which 90% of the scores lie. This is done using the quantile function, which is typically represented in statistical software like R. The appropriate code to use in this scenario is qt(0.9,10), which will give you the t value at the 90th percentile for 10 degrees of freedom.

The function qt() is used in R to obtain quantiles from a specified t-distribution. The first argument is the probability (in this case, 0.9 for the 90th percentile), and the second argument is the degrees of freedom (here, 10). Since we are dealing with the lower tail and want the value a for which P(X≤a)=0.9, we do not need to set 'lower.tail = FALSE' because it is for the upper tail of the distribution.