A carpet company advertises that it will deliver your carpet

A carpet company advertises that it will deliver your carpet within 16 days of purchase. The standard deviation of the population is known to be 5.6 days. A sample of 64 past customers is taken. The average delivery time in the sample was 17.1 days. Determine whether the mean of all delivery takes longer than what the company advertised. Use a = .04. State the null and alternative hypotheses. H0: H1: What is the critical value of the test? Using the critical value approach, test the hypotheses H0.

Solution

Given that a carpet company advertise that it will deliver your carpet within 16 days of purchase.

The hypothesis fir the testing is,

H₀ : µ = 16 Vs H₁ : µ > 16

This is the one tailed right sided test.

given that   = 0.04

population standard deviation () = 5.6 days

number of past customers (n) = 64

average delivery time in the sample (Xbar) = 17.1 days

Critical value of the test :

critical value can be calculated by using EXCEL.

Syntax = \"=NORMSINV(probability)

probability = 1 - = 1 - 0.04 = 0.96

We get critical value = 1.7507

Here population standard deviation is known and sample size is large so here we use Z-test.

The test statistic is,

Z = (Xbar - µ) / (/sqrt(n))

= (17.1-16) / (5.6 / sqrt(64) )

= 1.5714

Decision : Z < critical value

Conclusion : Accept H₀ at 4% level of significance.

A carpet company advertise that it will deliver your carpet within 16 days of purchase.