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 ?

We reject null hypothesis.

Step-by-step 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, : p 3.6%  {means that % of Viridian chairs arrive without all the parts is greater than or equal to 3.6%}

Alternate Hypothesis, : 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. =  ~ N(0,1)

where, = % of Viridian chairs arrive without all the parts in a testing of

                 500 chairs = 1%

          n  = sample of chairs = 500

So, test statistics =  

                              = -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.

TS is 24 units

Explanation:

ΔTRS and ΔSTQ are right angle triangle

Using pythagoras theorm:

(3x)² = (TR)² + (12)²

(3x)² = (18)² - (QT)²

(18)² - (QT)² = (TR)² + (12)²

180 = (TR)² + (QT)²

36 = (QT)² - (TR)²

QT² = 144

QT = 12

ΔTRS and ΔQRT are similar

Therefore, TS is 24 units