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TEA [102]
3 years ago
5

D is the wrong answer please help :(

Mathematics
2 answers:
Stella [2.4K]3 years ago
8 0

This can be solved by Newton's binomial formula

Tk+1 = (n k) a∧(n-k) b∧k  k+1=7 => k=6, n=11 , a=-3x and b=-2y

T7= (11 6) (-3x)∧(11-6) (-2y)∧6 = (11*10*9*8*7)/(1*2*3*4*5) (-3x)∧5 (-2y)∧6

T7= 462 (-3x)∧5 (-2y)∧6

The correct answer is A.

Good luck!!!


Viktor [21]3 years ago
7 0

\displaystyle T_r=\binom{n}{r-1}x^{n-r+1}y^{r-1}\\\\\\T_7=\binom{11}{6}(-3x)^{11-7+1}(-2y)^{7-1}\\\\T_7=\dfrac{11!}{6!5!}(-3x)^5(-2y)^6\\\\T_7=\dfrac{7\cdot8\cdot9\cdot10\cdot11}{2\cdot3\cdot4\cdot5}(-3x)^5(-2y)^6\\\\T_7=462(-3x)^5(-2y)^6

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in a program designed to help patients stop smoking 232 patients were given sustained care and 84.9% of them were no longer smok
grandymaker [24]

Answer:

z=\frac{0.849 -0.8}{\sqrt{\frac{0.8(1-0.8)}{232}}}=1.869  

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Step-by-step explanation:

1) Data given and notation

n=232 represent the random sample taken

X represent the adults were no longer smoking after one month

\hat p=0.849 estimated proportion of adults were no longer smoking after one month

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\alpha=0.05 represent the significance level

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z would represent the statistic (variable of interest)

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2) Concepts and formulas to use  

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When we conduct a proportion test we need to use the z statistic, and the is given by:  

z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}} (1)  

The One-Sample Proportion Test is used to assess whether a population proportion \hat p is significantly different from a hypothesized value p_o.

3) Calculate the statistic  

Since we have all the info requires we can replace in formula (1) like this:  

z=\frac{0.849 -0.8}{\sqrt{\frac{0.8(1-0.8)}{232}}}=1.869  

4) Statistical decision  

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.  

The significance level provided \alpha=0.05. The next step would be calculate the p value for this test.  

Since is a bilateral test the p value would be:  

p_v =2*P(Z>1.869)=0.0616  

If we compare the p value obtained and the significance level given \alpha=0.05 we see that p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of adults were no longer smoking after one month is not significantly different from 0.8 or 80% .  

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