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statuscvo [17]
3 years ago
10

A fancy new brand of laundry detergent just launched an aggressive advertisement campaign in the hope that people will use the b

rand despite its higher price point. An avid consumer is trying to determine whether this fancy new brand of laundry detergent cleans clothes better than his regular brand of laundry detergent. To do this, over the course of a month he randomly uses one of the detergents in each load of laundry and then, when the wash cycle is complete, assigns a value to how clean the clothes are based on the number of garments that are "sufficiently clean," with higher scores being better. If the consumer were to perform a test to tell the difference between the mean scores of each detergent (ignoring the flaws in this test design), what hypothesis would he use?
Mathematics
1 answer:
Fudgin [204]3 years ago
6 0

Step-by-step explanation:

Here is the answer to this question,

His hypothesis would be:

Null hypothesis:

H0: μ(new) - μ(regular) = 0

Alternate hypothesis:

H1: μ(new) - μ(regular) > 0

The consumer is testing to know if his new detergent is better off in cleaning than the regular. The question says that higher scores after cleaning is used to signify which is better based on sufficiently clean garment. Since he is interested in knowing the mean scores of the differences, he should use the hypothesis I stated above.

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Find the value of x and y.
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2 years ago
A psychologist obtains a random sample of 2020 mothers in the first trimester of their pregnancy. The mothers are asked to play
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First of all, we need to determine the system of hypothesis, which must have a null and alternative hypothesis.

In all hypothesis proof procedure, we must work with the null one, rejecting it or accepting it. If we reject the null hypothesis, it will mean that our principal hypothesis is true.

According to the problem, the null hypothesis must be: H_{o} : u = 100; because it says that 100 is the normal mean that is used.

The alternative hypothesis must be: H_{a} : u > 100; because the question is asking if there's enough evidence to say that they children have a higher IQ than 100.

Then, we must calculate the P-value, which is the probability value that we are gonna use to accept or reject the null hypothesis. This P-value we can calculate it with the formula: Z=\frac{x-u}{\frac{o}{\sqrt{n} } }; where x is the sample mean, u is the hypothetical mean parameter, o is the sample deviation and n is the sample.

Extracting all values from the problem: x = 104.3; u = 100; o = 14 and n = 20.

Applying all values to the formula: Z=\frac{104.3 - 100}{\frac{14}{\sqrt{20} } } = \frac{4.3}{\frac{14}{ 4.5} }=\frac{4.3}{3.1}=1.4

Then, this Z-value will give us the P-value by using the Z-table with the 0.05 level of significance. In table attached, we can see that the result is 0.9265. However, the P-value is 1 - 0.9265 = 0.735. We need to do this subtraction because, the result 0.9265 belong to the bigger area (as it's shown is the image in blue colour), and we need the smaller area, which belong to the 0.05 level of significance.

<em>In this problems, if the P-value is more than the level of significance, the null hypothesis is accepted. If the P-value is less than the level of significance the null hypothesis is rejected.</em>

Therefore, there is no enough evidence to say that the sample children have higher IQs, because the P-value is higher than the level of significance. (0.735>0.05).

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