Mathematics, 04.12.2020 16:50 groundcontrol

Chegg construct the 95% confidence interval for the difference between the positive rates of men and women.

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Answer from: madisyn13

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In a random sample of 700 men tested for the coronavirus, 63 were positive. Another independent random sample of 2950 women tested for the coronavirus resulted in 7 positive cases.Construct the 95% confidence interval for the difference between the positive rates of men and women

The 95% confidence interval is 0.833< p_1 - p_2 < 0.1059

Step-by-step explanation:

From the question we are told that

The sample size of men is n_1 = 700

The number men that tested positive is x_1 = 63

The sample size of women is n_2 = 2950

The number of women that tested positive is x_2 = 7

From the question we are told the confidence level is 95% , hence the level of significance is

$\alpha = (100 - 95 ) \%$

=> $\alpha = 0.05$

Generally from the normal distribution table the critical value of $\frac{\alpha }{2}$ is

$Z_{\frac{\alpha }{2} } = 1.96$

Generally the proportion of men that tested positive is mathematically represented as

$\^ p_1 = \frac{ x_1 }{n_1}$

=> $\^ p_1 = \frac{ 68 }{700}$

=> $\^ p_1 = 0.097$

Generally the proportion of women that tested positive is mathematically represented as

$\^ p_2 = \frac{ x_2 }{n_2}$

=> $\^ p_2 = \frac{ 7 }{2950}$

=> $\^ p_2 = 0.00237$

Generally the pooled population proportion is mathematically represented as

$\^ p = \frac{x_1 + x_2 }{ n_1 + n_2}$

=> $\^ p = \frac{ 63 + 7 }{ 700 + 2950}$

=> $\^ p = 0.0192$

Generally the standard error is mathematically represented as

$SE = \sqrt{\^ p (1- \^ p ) [ \frac{1}{n_1} + \frac{1}{n_2} ]}$

=> $SE = \sqrt{ 0.0192(1- 0.0192 ) [ \frac{1}{700} + \frac{1}{2950} ]}$

=> SE = 0.00577

Generally the margin of error is mathematically represented as

$E = Z_{\frac{\alpha }{2} } * SE$

=> E = 1.96 * 0.00577

=> E = 0.0113

Generally 95% confidence interval is mathematically represented as

$(\^ p_1 - \^ p_2 )-E < p_1 - p_2 < \^( p_1 - \^ p_2) + E$

=> (0.097 - 0.00237 )-0.0113< p_1 - p_2 < (0.097 - 0.00237 )+ 0.0113

=> 0.833< p_1 - p_2 < 0.1059

Answer from: Quest

you probably already have the answer but anyways it's b. 15.0

step-by-step explanation:

Answer from: Quest

6,250

step-by-step explanation:

to get the area, multiply 360 by 160.(57,600)

to find out how many bags of fertilizer it will take, first figure out how many square feet one bag can hold. divide 1000 by 8(125) to get the unit rate(how many square feet one pound of fertilizer can hold)and multiply it by 50(6250). if i haven't made a mistake, that is the answer.

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