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Mashcka [7]
2 years ago
10

Nan Compos-Mentis, a technical consultant, claims that she can increase average hourly productivity for the fabricators at Stryk

er Manufacturing by more than 10 units per worker. To support her claim, Nan plans to select a sample of workers, provide the workers in the sample with special training, and then use results from the sample in a hypothesis test designed to establish whether the training has had the desired effect. What null and alternative hypotheses would you recommend here?
Mathematics
1 answer:
dybincka [34]2 years ago
4 0

Answer:

H_0:  \bar X = 10\\H_a: \bar X >10

Step-by-step explanation:

given that Nan Compos-Mentis, a technical consultant, claims that she can increase average hourly productivity for the fabricators at Stryker Manufacturing by more than 10 units per worker.

To support her claim, Nan plans to select a sample of workers, provide the workers in the sample with special training, and then use results from the sample in a hypothesis test designed to establish whether the training has had the desired effect.

Here her matter of interest is whether training improves the mean score of hourly productivity

Hence the hypotheses should be

H_0:  \bar X = 10\\H_a: \bar X >10

A right tailed test.

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Identify whether the series sigma notation infinity i=1 15(4)^i-1 is a convergent or divergent geometric series and find the sum
const2013 [10]

Answer:  The correct option is

(d) This is a divergent geometric series. The sum cannot be found.

Step-by-step explanation: The given infinite geometric series is

S=\sum_{i=1}^{\infty}15(4)^{i-1}.

We are to identify whether the given geometric series is convergent or divergent. If convergent, we are to find the sum of the series.

We have the D' Alembert's ratio test, states as follows:

Let, \sum_{i=1}^{\infty}a_i is an infinite series, with complex coefficients a_i and we consider the following limit:

L=\lim_{i\rightarrow \infty}\dfrac{a_{i+1}}{a_i}.

Then, the series will be convergent if  L < 1 and divergent if  L > 1.

For the given series, we have

a_i=15(4)^{i-1},\\\\a_{i+1}=15(4)^i.

So, the limit is given by

L\\\\\\=\lim_{i\rightarrow \infty}\dfrac{a_{i+1}}{a_i}\\\\\\=\lim_{i\rightarrow \infty}\dfrac{15(4)^i}{15(4)^{i-1}}\\\\\\=\lim_{i\rightarrow \infty}\dfrac{15(4)^i}{15(4)^{i}4^{-1}}\\\\\\=\dfrac{1}{4^{-1}}\\\\=4>1.

Therefore, L >1, and so the given series is divergent and hence we cannot find the sum.

Thuds, (d) is the correct option.

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