Factorise<br> answer is (a+c) (ca-b²)

National data in the 1960's showed that about 44% of the adult population had never smoked cigarettes. In 1995 a national health

Marta_Voda [28]

Answer:

a) $0.52 - 1.96\sqrt{\frac{0.52(1-0.52)}{881}}=0.487$

$0.52 + 1.96\sqrt{\frac{0.52(1-0.52)}{881}}=0.553$

The 95% confidence interval would be given by (0.487;0.553)

b) After see the confidence interval we see that the lower limits 0.487>0.44 with 0.44 or 44% the estimated proportion for 1960, we can conclude that we have a significant increase in the adult proportion had never smoked cigarettes.

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Solution to the problem

Part a

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by:

$z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96$

The confidence interval for the mean is given by the following formula:

$\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$

If we replace the values obtained we got:

$0.52 - 1.96\sqrt{\frac{0.52(1-0.52)}{881}}=0.487$

$0.52 + 1.96\sqrt{\frac{0.52(1-0.52)}{881}}=0.553$

The 95% confidence interval would be given by (0.487;0.553)

Part b

After see the confidence interval we see that the lower limits 0.487>0.44 with 0.44 or 44% the estimated proportion for 1960, we can conclude that we have a significant increase in the adult proportion had never smoked cigarettes at 5% of significance.

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Approximate square root of 800 to the nearest hundredth

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28.30 is the square root of 800

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3 years ago

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A recent census listed the population of a city as 831,982.Marisol rounds the population to 83000 and lindy rounds the populatio

lbvjy [14]

In this question, lindy rounds the population correctly.
The numbers 831,982 and 800000 are both six- digit numbers. But 83000 is a five- digit number.
And 831,982 rounded to nearest lakh is 800000.

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3 years ago

A businesswoman wants to determine the difference between the costs of owning and leasing an automobile. She can lease a car for

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First we need to find the total annual costs for both the plans.

In case of leasing:
Fixed monthly cost = $420
So, yearly cost = 420 x 12 = $5040
Cost per mile = $0.08

For x miles driven, the cost per year for leasing will be = 5040 + 0.08x

In case of purchasing:
Fixed yearly cost = $4600
Cost per mile = 0.10

For x miles driven, the cost per year for leasing will be = 4600 + 0.10x

We want to find for what number of miles will the cost of leasing will be no more expensive than the cost of purchasing.

So,

Cost of leasing ≤ Cost of purchasing
5040 + 0.08x ≤ 4600 + 0.10x
440 ≤ 0.02x
22000 ≤ x

Thus, if if the number of miles driven are equal to or less than 22,000 leasing will be no more expensive than purchasing.

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A pair of jeans is on sale 20% off. The sale price is $32. What is the regular price?

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Original price: $40.00
Saved amount: $8.00

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Factorise answer is (a+c) (ca-b²)​

Factorise answer is (a+c) (ca-b²)