Question

Tango Furniture sells furniture online, arriving at customers homes needing to be assembled. Suppose 3.6% of their Viridian chairs arrive without all the parts. In trying to improve the system, Hakim reorganizes the packaging system of the Viridian and after testing 500 chairs, only 1% have missing parts.

Is this result a statistically significant improvement?

Fail to reject the null hypothesis or reject null hypothesis ?

Answer 1

We reject null hypothesis.

Explanation:

We are given that Tango Furniture sells furniture online, arriving at customers homes needing to be assembled. Suppose 3.6% of their Viridian chairs arrive without all the parts.

In trying to improve the system, Hakim reorganizes the packaging system of the Viridian and after testing 500 chairs, only 1% have missing parts.

We have to test is this result a statistically significant improvement.

Let p = % of Viridian chairs arrive without all the parts

SO, Null Hypothesis,
`H_0` : p
`\geq` 3.6% {means that % of Viridian chairs arrive without all the parts is greater than or equal to 3.6%}

Alternate Hypothesis,
`H_a` : p < 3.6% {means that % of Viridian chairs arrive without all the parts is less than 3.6%}

The test statistics that will be used here is One-sample z proportion statistics;

T.S. =
`\frac{\hat p-p}{\sqrt{(\hat p(1- \hat p))/(n) } }` ~ N(0,1)

where,
`\hat p` = % of Viridian chairs arrive without all the parts in a testing of

500 chairs = 1%

n = sample of chairs = 500

So, test statistics =
`\frac{0.01-0.036}{\sqrt{(0.01(1- 0.01))/(500) } }`

= -5.843

Since in the question we are not given with the significance level so we assume it to be 5%. So, at 0.05 level of significance, the z table gives critical value of -1.6449 for one-tailed test. Since our test statistics is less than the critical value of z so we have sufficient evidence to reject null hypothesis as it will fall in the rejection region.

Therefore, we conclude that % of Viridian chairs arrive without all the parts is less than 3.6% which means that there is statistically significant improvement.