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NemiM [27]
3 years ago
7

The quality control manager of a soda manufacturing company wishes to use a significant level of 0.05 to test whether the variab

ilities in the amount of soda in the company's 16 OZ bottles is more than the variabilities in the company's 12 OZ bottles. The following two samples have been randomly collected. What is the critical value of this hypothesis testing problem?
Mathematics
2 answers:
Alex17521 [72]3 years ago
6 0

Answer: 1.645

Step-by-step explanation:

Given : The quality control manager of a soda manufacturing company wishes to use a significant level of 0.05 to test whether the variabilities in the amount of soda in the company's 16 OZ bottles is more than the variabilities in the company's 12 OZ bottles.

Let \sigma_1^2 represents the variance for 16 OZ bottles and \sigma_2^2 represents the variance for 12 OZ bottles.

The Null and Alternative Hypothesis will be  :-

H_0:\sigma_1^2\geq\sigma_2^2

H_1:\sigma_1^2, since alternative hypothesis is left-tailed , then the test is left-tailed test.

By using the standard normal distribution table for z, the critical value for this hypothesis:-

z_{\alpha}=z_{0.05}=1.645

Alik [6]3 years ago
5 0

Answer:

1.6

Step-by-step explanation:

the significant level = 0.05

the sample number of the bottles = 12 bottles

The number of bottles randomly selected = 2

Therefore, the critical value for the hypothesis to be accepted  = 1.6

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We have been given that Layana’s house is located at (2\frac{2}{3}, 7\frac{1}{3}) on a map. The store where she works is located at (-1\frac{1}{3}, 7\frac{1}{3}).

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We will use distance formula to solve our given problem.

Let us convert our given coordinates in improper fractions.

2\frac{2}{3}\Rightarrow \frac{8}{3}

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Now we will use distance formula to solve our given problem.

D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

Upon substituting coordinates of our given point in above formula, we will get:

D=\sqrt{(\frac{22}{3}-\frac{22}{3})^2+(\frac{8}{3}-(-\frac{4}{3}))^2}

D=\sqrt{(0)^2+(\frac{8}{3}+\frac{4}{3})^2}

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D=\sqrt{(\frac{12}{3})^2}

D=\sqrt{(4)^2}

D=4

Therefore, the distance from Layana's home to the store is 4 units and option A is the correct choice.

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3 years ago
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If A and B are supplementary angles, then:
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