To make this equation true we need parentheses
1 answer:
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Answer:
a)
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 and
. And the critical value would be given by:
The confidence interval for the mean is given by the following formula:
If we replace the values obtained we got:
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.
Statement Reason
1. Given
2. Distributive property of multiplication over addition
Let 'a', 'b' and 'c' be any real numbers. So, Distributive property of multiplication over addition states a(b+c) = ab + ac
3. Subtraction property of order
4. Addition property of equality
The addition property of equality states that if the same number is added to both sides of an equation, then the equation is still true.
5. x<1 Division property of equality
The Division Property of Equality states that if you divide both sides of an equation by the same nonzero number, the equation remain equal.