math statistic mat205

Question

- Consider a t distribution with 9  degrees of freedom. Compute  P≤t−1.4 . Round your answer to at least three decimal places.P(t≤−1.4 )=

 

(b)Consider a t distribution with 16  degrees of freedom. Find the value of c such that 

P(−c<t<c)=0.95 . Round your answer to at least three decimal places.

Answer 1

a) Using https://stattrek.com/online-calculator/t-distribution and inputting our degrees of freedom and t-statistic, we get that P(t≤−1.4) = 0.09751

b) We want to find a value c such that 95% of the observations generated by a t-distribution lie would lie between -c and c. In other words, we want to find a value of c such that 0.025% of observations are above c and another 0.025% of observations are below -c, as then 95% of observations will be bounded by -c and c and 5% will be in the "tails" of the distribution. Using https://www.tdistributiontable.com/, we see that for a t-distribution with 16 degrees of freedom, a t-statistic of 2.120 has 5% of observations in the "tails". Thus, c = 2.120.

Answer 2

a) Use technology, like a graphing calculator, or find a t calculator online or use a t chart to find that P(t₉<-1.4) is .145. The information is from the area of the t cdf that indicates areas less than -1.4.

b) The easiest way is to find the inverse t₁₆ values that gives you a probability of .025 in one of the tails. This gives you c or -c and the interval is constructed. (-c = -2.120)

Please consider a tutor. Take care.