Question

HYPOTHESES IN THE REAL WORLD: Consider a business of any type. What is a situation where a hypothesis test might help make a decision? Describe the situation. Then you or someone in a reply can make up numbers for that situation and someone else can solve it.

Answer 1

Let us consider a Printing Business.

Suppose the business claims that each ink cartridge prints 1000 pages. Thus it can be a situation where a hypothesis test might help make a decision.

Let the no. of pages each ink cartridge printed over a span of a yeary be as follows:

1024 976 1096 936 985 1004 1105

Can the business have 95 % confidence that the mean no. of pages each ink cartridge prints is not 1000?

Solution:

null hypothesis: H ₀: μ = 1000

alternative hypothesis: H _a: not H ₀

_{And we can perform one sample t-test in R using the code:}

x<-(1024,976,1096,936,985,1004,1105)

t.test(x, mu = 1000, alternative = "two.sided")

Decision Rule:

We will reject H_{​​​​​​0} at 5% level of significance if p-value is less than 0.05.