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bogdanovich [222]
3 years ago
14

A random sample of 20 purchases showed the amounts in the table (in $). The mean is $49.57 and the standard deviation is $20.28.

Construct a 98​% confidence interval for the mean purchases of all​ customers, assuming that the assumptions and conditions for the confidence interval have been met.
Mathematics
1 answer:
son4ous [18]3 years ago
3 0

Answer:

The 98​% confidence interval for the mean purchases of all​ customers is ($37.40, $61.74).

Step-by-step explanation:

We have that to find our \alpha level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\alpha = \frac{1-0.98}{2} = 0.01

Now, we have to find z in the Ztable as such z has a pvalue of 1-\alpha.

So it is z with a pvalue of 1-0.01 = 0.99, so z = 2.325

Now, find M as such

M = z*\frac{\sigma}{\sqrt{n}}

In which \sigma is the standard deviation of the population and n is the size of the sample.

M = 2.325*\frac{20.28}{\sqrt{20}} = 12.17

The lower end of the interval is the mean subtracted by M. So it is 49.57 - 12.17 = $37.40.

The upper end of the interval is the mean added to M. So it is 49.57 + 12.17 = $61.74.

The 98​% confidence interval for the mean purchases of all​ customers is ($37.40, $61.74).

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Step-by-step explanation:

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We substitute our given values to calculate the sample size:

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Answer:

FIRST EXPRESSION:

-  If b=-3, the value of 4b(b+1) is  24

-  If b=-2, the value of 4b(b+1) is  8

- If b=10, the value of 4b(b+1) is  440

 SECOND EXPRESSION:

-  If b=-3, the value of (2b+7)(2b-8)) is  -14

-  If b=-2, the value of (2b+7)(2b-8)) is  -36

- If b=10, the value of (2b+7)(2b-8)) is  324

Yes, for any value of "b" the value of the first expression is greater than the value of the second expression.

Step-by-step explanation:

Substitute the given values of "b" into each expression and evaluate.

- For the first expression 4b(b+1), you get:

If b=-3 → 4(-3)(-3+1)=24

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 - For the second expression (2b+7)(2b-8)), you get:

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If b=-2 → (2(-2)+7)(2(-2)-8)=-36

 If b=10 → (2(10)+7)(2(10)-8)=324

You can observe that for any value of "b" the value of the first expression is greater than the value of the second expression.

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