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kolezko [41]
3 years ago
15

An article in the November 1983 Consumer Reports compared various types of batteries. The average lifetimes of Duracell Alkaline

AA batteries and Eveready Energizer Alkaline AA batteries were given as 4.1 hours and 4.5 hours, respectively. Suppose these are the population average lifetimes. (a) Let X be the sample average lifetime of 81 Duracell and Y be the sample average lifetime of 81 Eveready Energizer batteries.
What is the mean value of X − Y (i.e., where is the distribution of X − Y centered)?
Does your answer depend on the specified sample sizes?

A. The answer increases as the sample size decreases.
B. The answer is the same irrespective of the sample sizes.
C. The answer decreases as the sample size increases.
D. The answer decreases as the sample size decreases.
E. The answer increases as the sample size increases.
Mathematics
1 answer:
Tamiku [17]3 years ago
4 0

Answer:

-0.4

B. The answer is the same irrespective of the sample sizes.

Step-by-step explanation:

Given that an article in the November 1983 Consumer Reports compared various types of batteries. The average lifetimes of Duracell Alkaline AA batteries and Eveready Energizer Alkaline AA batteries were given as 4.1 hours and 4.5 hours, respectively

Let X be the sample average lifetime of 81 Duracell and Y be the sample average lifetime of 81 Eveready Energizer batteries.

Now we have sample mean difference does not depend about the sample sizes.

This is because

E(X-Y) = E(X)-E(Y) for all X and Y

Mean of X-Y = 4.1-4.5=-0.4

This does not depend on the specified sample sizes

B. The answer is the same irrespective of the sample sizes.

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From generation to generation, the mean age when smokers first start to smoke was believed to be 17. A survey of 40 smokers of t
melamori03 [73]

Answer:

(17.6962, 18.5038)

Since 17 does not lie in this interval, we reject the first start was at age 17.

The confidence interval implies we are 95% confident that for large sample sizes, randomly drawn sample mean will fall within this interval.

Step-by-step explanation:

Given that from generation to generation, the mean age when smokers first start to smoke was believed to be 17.

A survey of 40 smokers of the millennial generation was done to see if the mean starting age is now different.

The sample mean is 18.1 with a sample standard deviation of 1.3.

We get mean difference =1.1

Std error = \frac{1.3}{\sqrt{40} } \\=0.206

Z critical value for 95% = 1.96

Margin of error =1.96 ( std error) = 0.40376

Confidence interval

=(18.1-0.4038, 18.1+0.4038)\\= (17.6962, 18.5038)

Since 17 does not lie in this interval, we reject the first start was at age 17.

The confidence interval implies we are 95% confident that for large sample sizes, randomly drawn sample mean will fall within this interval.

7 0
4 years ago
Consider the rectangle shown
emmainna [20.7K]

Step-by-step explanation:

<em>Perimeter </em><em>of </em><em>a </em><em>rectangle</em><em>=</em><em> </em><em>2</em><em>L</em><em> </em><em>+</em><em> </em><em>2</em><em>W</em>

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