# A new machine is purchased by a pastry shop which will be utilized to fill the insides of various pastries. A test run is commissioned in which the following proportions of jelly are inserted into each pastry. We are tasked with finding the 90% confidence interval for the mean filling amount from this process. #

**s <- c(.28,.25,.22,.20,.33,.20)**

w <- sd(s) / sqrt(length(s))

w <- sd(s) / sqrt(length(s))

**w**

*[1] 0.02092314*

**degrees <- length(s) - 1**

**degrees**

*[1] 5*

**t <- abs(qt(0.05, degrees))**

**t**

*[1] 2.015048*

**m <- (t * w)**

**m**

*[1] 0.04216114*

**mean(s) + c(-m, m)**

*[1] 0.2045055 0.2888278*

# We can state, with 90% confidence, that the machine will insert into pastries proportions of filling between .205 and .289. In the above execise, a new concept is introduced in step 4. The abs() function, in conjunction with the qt() function, allows you to find Critical-T values through the utilization of R without having to refer to a textbook. A few examples as to how this function can be utilized are listed below. #

# T VALUES (Confidence / Degrees of Freedom ) #

**abs(qt(0.25, 40))**# 75% confidence, 40 degrees of freedom, 1 sided (same as

**qt(0.75, 40))**#

**abs(qt(0.01, 40))**# 99% confidence, 40 degrees of freedom, 1 sided (same as

**qt(0.99, 40))**#

**abs(qt(0.01/2, 40))**# 99% confidence, 40 degrees of freedom, 2 sided #

I hope that you found this abbreviated article to be interesting and helpful. Until next time, I'll see you later Data Heads!

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