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 ##################

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