SOLUTION: Increasing numbers of businesses are offering child-care benefits for their workers. However, one union claims that more than 80% of firms in the manufacturing sector still do not

Question 444954: Increasing numbers of businesses are offering child-care benefits for their workers. However, one union claims that more than 80% of firms in the manufacturing sector still do not offer any child-care benefits to their workers. A random sample of 300 manufacturing firms is selected, and only 29 of them offer child-care benefits. Test the union's claim at a=0.05

A local supermarket claims that the variance of waiting time for its customers to be served is the lowest in the area. A competitor checks the waiting time at both supermarkets. The sample statistics are listed below. Test the claim at a=0.05.
(local supermarket: n1=13, s1= 1.21 minutes)
(competitor: n2=16, s2=1.43 minutes)
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Increasing numbers of businesses are offering child-care benefits for their workers. However, one union claims that more than 8% of firms in the manufacturing sector still do not offer any child-care benefits to their workers. A random sample of 300 manufacturing firms is selected, and only 29 of them offer child-care benefits. Test the union's claim at a=0.05
--------------------------
Ho: p <= 0.08
Ha: p > 0.08 (union claim)
---
p-hat = 29/300 = 0.097
------
z(0.097)=(0.097-0.08)/sqrt[0.08*0.92/300] = 1.085352..
------
p-value = P(z > 1.085352) = 0.1389
----
Since the p-value is greater than 5%, fail to
reject Ho. The test results do not support
the union claim.
=======================================================

A local supermarket claims that the variance of waiting time for its customers to be served is the lowest in the area. A competitor checks the waiting time at both supermarkets. The sample statistics are listed below. Test the claim at a=0.05.
(local supermarket: n1=13, s1= 1.21 minutes)
(competitor:::::::: n2=16, s2=1.43 minutes)
-----------
Ho: s2^2-s1^2 <= 0
Ha: s2^2-s1^2 > 0 (local supermarket claim)
------------
I ran a 2-Sample F-Test on the data and got the following:
test statistic: F = 1.39669...
p-value = 0.2832
---
Since the p-value is greater than 5%, fail to reject Ho.
The test results do not support the local supermarket claim.
================================
Cheers,
Stan H.

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