Mathematics, 12.08.2020 06:01 merrylsimpson

A survey asked, "How many tattoos do you currently have on your body?" Of the males surveyed, responded that they had at least one tattoo. Of the females surveyed, responded that they had at least one tattoo. Construct a % confidence interval to judge whether the proportion of males that have at least one tattoo differs significantly from the proportion of females that have at least one tattoo. Interpret the interval.

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Answer from: CAPEPOPPA

Complete Question

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The 95% interval for p_1 - p_2 is -0.0171 ,0.0411

Option A is correct

Step-by-step explanation:

From the question we are told that

The sample size of male is n_1 = 1211

The number of males that said they have at least one tattoo is r = 182

The sample size of female is n_2 = 1041

The number of females that said they have at least one tattoo is k = 144

Generally the sample proportion of male is

$\r p_1 = \frac{r}{ n_1}$

substituting values

$\r p_1 = \frac{ 182}{1211}$

$\r p_1 = 0.1503$

Generally the sample proportion of female is

$\r p_2 = \frac{k}{ n_2}$

substituting values

$\r p_2 = \frac{ 144}{1041}$

$\r p_2 = 0.1383$

Given that the confidence level is 95% then the level of significance is mathematically represented as

$\alpha =100-95$

$\alpha =5\%$

$\alpha =0.05$

Next we obtain the critical value of $\frac{\alpha }{2}$ from the normal distribution table , the value is

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

Generally the margin of error is mathematically represented as

$E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\r p_1 (1- \r p_1)}{n_1} + \frac{\r p_2 (1- \r p_2)}{n_2} }$

substituting values

$E = 1.96 * \sqrt{\frac{ 0.1503 (1- 0.1503)}{1211} + \frac{0.1383 (1- 0.1383)}{1041} }$

E = 0.0291

The 95% confidence interval is mathematically represented as

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

substituting values

(0.1503- 0.1383 ) - 0.0291 < p_1-p_2 < (0.1503- 0.1383 ) + 0.0291

-0.0171 < p_1-p_2 < 0.0411

So the interpretation is that there is 95% confidence that the difference of the proportion is in the interval .So conclude that there is insufficient evidence of a significant difference in the proportion of male and female that have at least one tattoo

This because the difference in proportion is less than $\alpha$

A survey asked, How many tattoos do you currently have on your body? Of the males surveyed, respon

Answer from: Quest

the answer will be b x² +x-1

step-by-step explanation:

Answer from: Quest

First locate the turning point (vertex) of the graph. which is at the coordinates x=5 and y=9 or (5; 9).to determine whether it's a maximum or mininum value, you have to discern whether the vertex's y-value is the highest value or lowest value the graph can reach. since the vertex's y-value, 9 is the highest value the graph can reach, it will be a maximum.another basic way to determine whether the vertex's value is max or min is to see if the graph is smiling or sad. if it's smiling, the turning point/vertex would be a minimum, while a sad parabola would have a maximum y-value at the vertex.

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A survey asked, "How many tattoos do you currently have on your body?" Of the males surveyed, respon...