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Anastasy [175]
3 years ago
15

1.5 cups per day how many gallons per weeek? (1gallon =16cup)

Mathematics
1 answer:
anyanavicka [17]3 years ago
8 0
So as you know, one gallon has 16 cups, and there's 7 days in a week. So, if you multiple 1.5 by 7 you would get 10.5 cups per week, then divide that by 16 and get .65625 gallons per week.
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At a large Midwestern university, a simple random sample of 100 entering freshmen in 1993 found that 20 of the sampled freshmen
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The 90% confidence interval for the difference of proportions is (0.01775,0.18225).

Step-by-step explanation:

Before building the confidence interval, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

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When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

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p_1 = \frac{20}{100} = 0.2

s_1 = \sqrt{\frac{0.2*0.8}{100}} = 0.04

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p_2 = \frac{10}{100} = 0.1

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s = \sqrt{s_1^2+s_2^2} = \sqrt{0.04^2 + 0.03^2} = 0.05

Confidence interval:

p \pm zs

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z is the z-score that has a p-value of 1 - \frac{\alpha}{2}.

90% confidence level

So \alpha = 0.1, z is the value of Z that has a p-value of 1 - \frac{0.1}{2} = 0.95, so Z = 1.645.  

The lower bound of the interval is:

p - zs = 0.1 - 1.645*0.05 = 0.01775


The upper bound of the interval is:

p + zs = 0.1 + 1.645*0.05 = 0.18225


The 90% confidence interval for the difference of proportions is (0.01775,0.18225).

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