Harold stores 10,656 pounds of grain 24 cattle each row eats about 12 pounds of rain each day how many days with the food supply last

Answer:

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Answer is in the attached file.

Answer:

Less than 4% of a company's widgets are defective.

Step-by-step explanation:

In this case we want to be reasonably certain that less than 4% of a company's widgets are defective.

The significance level of the test is, α = 0.01.

The hypothesis can be defined as follows:  

H₀: At least 4% of a company's widgets are defective, i.e. p ≥ 0.04.  

Hₐ: Less than 4% of a company's widgets are defective, i.e. p < 0.04.  

The information provided is:  

n = 250

x = 6

The sample proportion is,

Compute the test statistic value as follows:  

The test statistic value is -1.29.  

The decision rule is:  

The null hypothesis will be rejected if the p-value of the test is less than the significance level.  

Compute the p-value as follows:  

So,

p-value = 0.0985 > α = 0.01.  

The null hypothesis will not be rejected at 1% significance level.  

Thus, there is not enough evidence to support the claim.

Conclusion:

Less than 4% of a company's widgets are defective.

Final answer:

This is a hypothesis testing problem where we test the claim that less than 4% of widgets are defective. We set the null and alternative hypotheses, confirm conditions for a binomial distribution, compute the test statistic, find the p-value and then make a conclusion based on the comparison of p-value with the given significance level.

Explanation:

In this scenario, we are interested in testing the hypothesis about the proportion of defective widgets. We define our null hypothesis (H0) and the alternative hypothesis (Ha) as follows:

H0: p = 0.04  (The proportion of defective widgets is 4%)

Ha: p < 0.04  (The proportion of defective widgets is less than 4%)

The conditions for a binomial distribution are met here, as each widget is either defective or not, and each widget is tested independently. Also, the quantities np and nq (where n is the sample size and q is the probability of failure) are greater than five, so we can approximate by the normal distribution.

We calculate the test statistic using the formula: z = (p' - p) / sqrt [ (p * q) / n ]

Where, p' is the sample proportion, which is 6/250, p is the hypothesized proportion which is 0.04, q is 1 - p and n is the sample size (250). This gives us a z value. Then, we find the p-value from the standard normal distribution using this z value. If p-value < α (0.01), we reject the null hypothesis. Otherwise, we do not reject it.

At the end, you will conclude. If we reject the null, we say, 'At the 1 percent significance level, there is sufficient evidence to conclude that less than 4% of the company's widgets are defective'. If we don't reject the null, 'At the 1 percent significance level, there is insufficient evidence to conclude that less than 4% of the company's widgets are defective.'

Learn more about Hypothesis testing here:

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The translation path of Point A (3, -8) to A'(-4,-5) exists 3 units down and 7 units to the left.

What is meant by translation?

A translation in mathematics does not turn, but rather moves a shape left, right, up, or down. Congruent translations are those in which the translated shapes (or the image) seem to be the same size as the source ones. Just one or more directions have they shifted.

Each point in a figure is moved by the same amount and in the same direction during a translation, a type of transformation.

With a sort of transformation called translation, every point in a figure is moved the same distance in the same direction.

The translation path of Point A (3, -8) to A'(-4,-5) exists 3 units down and 7 units to the left.

To learn more about translation, refer to:

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Answer:

left 7 and up 13

Step-by-step explanation: