Chegg A manufacturer of submersible pumps claims that at most 30% of the pumps require repairs within the first 5 years of operations. A random sample of 120 of these pumps included 47 which required repairs within the first 5 years. Does the manufacturer’s claim appear to be true, at the 0.05 level of significance?

No, the manufacturer’s claim doesn't appear to be true, at the 0.05 level of significance.

Step-by-step explanation:

We are given that a manufacturer of submersible pumps claims that at most 30% of the pumps require repairs within the first 5 years of operations. A random sample of 120 of these pumps included 47 which required repairs within the first 5 years.

We have to test the manufacturer’s claim.

Firstly, as we know that the testing is done always on the population parameter.

Let p = % of the pumps that require repairs within the first 5 years of operations.

SO, Null Hypothesis, : 30%  {means that at most 30% of the pumps require repairs within the first 5 years of operations}

Alternate Hypothesis, : p > 30%   {means that more than 30% of the pumps require repairs within the first 5 years of operations}

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

                    T.S. =  ~ N(0,1)

where, = proportion of the pumps that require repairs within the first 5 years of operations in a sample of 120 =

            n = sample of pumps  120

So, test statistics  =

                               = 2.057

Now, at 0.05 level of significance, the z table gives critical value of 1.6449. Since our test statistics is more than the critical value of z so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.

Therefore, we conclude that more than 30% of the pumps require repairs within the first 5 years of operations which means the manufacturer’s claim was not true.

560

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step-by-step explanation:

sin(7pi/6 - pi/3)  

= sin(7pi/6 - 2pi/6)  

= sin(5pi/6)  

= sin(pi - pi/6)  

= sin(pi/6)  

= 1/2  

sin 7pi/6 - sin pi/3  

= sin (pi + pi/6) - sin pi/3  

= -sin pi/6 - sin pi/3  

= -1/2 - sqrt(3)/2  

= -(1+sqrt(3))2