Question

Describe a real-world example of when a hypothesis test could be used and include a numerical example. The example can use real data or data that you make up, such as values for the mean, standard deviation, and sample size. Be sure to note if the standard deviation is from the population or the sample.

Answer 1

Suppose sweets are sold in package of fixed weight of the contents. The producer of the package is interested in testing that average weight of contents in package in 1kg. Hence a random sample of 12 packages is drawn and thier content found (in kg) as follows 1.05, 1.01, 1.04, 0.98, 0.96, 1.01, 0.97, 0.99, 0.98, 0.95, 0.97, 0.95

Using the above quantity what should conclude about the average weight of contents in the packets using 5%.

Here Ho, μ = 1 vs H1: μ ≠ 1

x̄= = = 0.9883

mean, x̄ = 0.9883

=

= = 0.0015273

Standard deviation, S = 0.03908

TS = = (0.9883-1) √12   = -1.0371

p-value = p[t<-1.0371] = 0.1299

p-value > 0.05

We accept Ho