Question

Write R code for to concule whether to accept or reject the null hypothesis for the following question:

A manufacturer claims that the thickness of the steel plates it produces is 61 mils (thousandth of an inch). Car manufacturer's quality control officer regularly checks the claim. From a recent shipment he took a random sample of 50 plates: the sample mean and variance are 61.3 and 1.22, respectively. In order to verify that the manufacturer's claim is accurate, what should his null hypothesis be and should it be accepted at 10% significance level?

Answer 1

Solution:

Here, we have to use one sample t-test for a population mean.

Null hypothesis: H₀: The thickness of the steel plates is 61 mils.

Alternative hypothesis: H_a: The thickness of the steel plates is different from 61 mils.

H₀: µ = 61 versus H_a: µ ≠ 61

Test statistic = t = (Xbar - µ)/[S/sqrt(n)]

We are given

Xbar = 61.3, S² =1.22, S = sqrt(1.22) = 1.104536, n=50, α = 0.10

Required R codes are given as below:

> xbar=61.3

> s=1.104536

> mu=61

> n=50

> t=(xbar - mu)/(s/sqrt(n))

> df= n-1

> p = dt(t,df)

> t

[1] 1.920553

> df

[1] 49

> p

[1] 0.06466888

We get P-value = 0.06 < α = 0.10

So, we reject the null hypothesis H₀

Null hypothesis should not be accepted at 10%

There is insufficient evidence to conclude that the thickness of the steel plates is 61 mils.