Mathematics, 08.04.2020 01:30 warnene17

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 ?

Answers: 1

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Answer from: HtetPaing9281

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, 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. = $\frac{\hat p-p}{\sqrt{\frac{\hat p(1- \hat p)}{n} } }$ ~ 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 = $\frac{0.01-0.036}{\sqrt{\frac{0.01(1- 0.01)}{500} } }$

= -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.

Answer from: Quest

113.1

step-by-step explanation:

v=4

3πr3=4

3·π·33≈113.09734

Answer from: Quest

answer: - (a) $a_n=16+6n$

(b) 88 seats

step-by-step explanation:

given: in an auditorium, there are 22 seats in the first row and 28 seats in the second row.

thus first term= $a_1 =22$

second term= $a_2 =28$

the number of seats in a row continues to increase by 6 with each additional row.

⇒d= 6

a) given formula : $a_n=a_1+(n-1)(d)$

$a_n=22+(n-1)6\\\rightarrow\ a_n=22+6n-6\\\rightarrow\ a_n=16+6n$

b) let the number of seats (n) = 12

substitute n=12 in the explicit rule formed in (a)

$a_{12} = 16+6\times12\\\rightarrow\ a_{12}=16+72\\\rightarrow\ a_{12}=88\ seats$

∴there are 88 seats in 12 rows.

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Tango Furniture sells furniture online, arriving at customers homes needing to be assembled. Suppose...