Question

**6) Find a 90% confidence interval for the true mean weight of all bolts produced by a particular machine in a factory. It is known from previous experimenting with this particular machine that the population standard deviation is 0.8**

```{r}
Bolts<-c(2.3, 2.7, 2.4, 2.2, 2, 4, 3, 3.3, 1.1, 2.1, 2, 2.9, 1.9, 3.2, 2.1, 3, 3.4, 1.1)

###Please do your work here###

##############################
```

**How would you interpret this confidence interval? Please type your answer on the line below**

Answer:

Answer 1

90% Confidence Interval for true mean = (2.4102, 2.5564)

We calculated CI with the help of R software.

R Code:

####################################
# x denotes bolts
x = c(2.3, 2.7, 2.4, 2.2, 2, 4, 3, 3.3, 1.1, 2.1, 2, 2.9, 1.9, 3.2, 2.1, 3, 3.4, 1.1)
sig = 0.8
z = qnorm(0.95, 0, 1)
### Confidence Interval for Population Mean #######
l = mean(x) - (z*(sig/length(x)));l
u = mean(x)+(z*(sig/length(x)));u
######### The End ##################
Output:

> ####################################
> # x denotes bolts
> x = c(2.3, 2.7, 2.4, 2.2, 2, 4, 3, 3.3, 1.1, 2.1, 2, 2.9, 1.9, 3.2, 2.1, 3, 3.4, 1.1)
> sig = 0.8
> z = qnorm(0.95, 0, 1)
> ### Confidence Interval for Population Mean #######
> l = mean(x)-(z*(sig/length(x)));l
[1] 2.410229
> u = mean(x)+(z*(sig/length(x)));u
[1] 2.556438
> ######### The End ##################