47 1/2% in simplest form
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c. Smoking is associated with lower birth weights. When smokers are compared to nonsmokers, we are 95% confident that the mean weight of babies born to nonsmokers will be between 76.5 grams to 486.9 grams more than the mean birth weight of babies born to smokers.
Step-by-step explanation:
The difference in mean birth weights (nonsmokers minus smokers) is 281.7 grams with a margin of error of 205.2 grams with 95% confidence.
Then, we know that the 95% confidence interval is (76.5, 486.9)
<em>a. We are 95% confident that smoking causes lower birth weights by an average of between 76.5 grams to 486.9 grams.</em>
False, it interprets the confidence interval as a probability for individual cases. The confidence interval is a range for the population mean.
<em>b. There is a 95% chance that if a woman smokes during pregnancy her baby will weigh between 76.5 grams to 486.9 grams less than if she did not smoke.</em>
False, it interprets the confidence interval as a probability for individual cases. The confidence interval is a range for the population mean.
<em>c. Smoking is associated with lower birth weights. When smokers are compared to nonsmokers, we are 95% confident that the mean weight of babies born to nonsmokers will be between 76.5 grams to 486.9 grams more than the mean birth weight of babies born to smokers.</em>
True.
<em>d. With such a large margin of error, this study does not suggest that there is a difference in mean birth weights when we compare smokers to nonsmokers.</em>
There is enough evidence, as the lower bound of the confidence is positive. This means that there is only a probability of 0.05/2=0.025 that the true mean weight difference is smaller than 76.5 grams.
The specified function's vertex form is
If a quadratic equation is written in the form
then it is called to be in vertex form. It is called so because when you plot this equation's graph, you will see vertex point(peak point) is on (h,k)
<h3>What is a perfect square polynomial?</h3>If a polynomial p(x) can be written as:
where f(x) is also a polynomial, then p(x) is called as perfect square polynomial
For the considered case, the polynomial specified is;
- Case 1: Converting to vertex form
Thus, the vertex form of the considered polynomial is
- Case 2: Converting to standard form
Standard form of a quadratic polynomial is
Thus, we get: the considered polynomial in standard form as:
- Case 3: Factoring the first two terms of polynomial
- Case 4: Forming a perfect square trinomial
The considered polynomial has only two terms, therefore, its not a trinomial.
Thus, the specified function's vertex form is
Learn more about vertex form of a quadratic equation here: