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.

"image"

step-by-step explanation:

in most of these problems, the notation is that the point with a "prime" is the image of the point without. that is, b' is the image of b.

here, there is no dilation or reflection. there is simply translation (with no direction shown). which figure you call the "preimage" and which one you call the "image" is up to you. as a matter of convention, the naming is as described above.