An article regarding interracial dating and marriage...

Name: an article regarding interracial dating and marriage recently appeared in the washington post of the 1709 randomly selected adults 315 identified themselves as latinos 323 identified themsel 61975
Uploaded: 2020-10-24T19:39:25-08:00
Duration: 12 min 23 s
Channel: Evelyn Cunningham
Description: an article regarding interracial dating and marriage recently appeared in the washington post of the 1709 randomly selected adults 315 identified themselves as latinos 323 identified themsel 61975

An article regarding interracial dating and marriage recently appeared in the Washington Post. Of the 1,709 randomly selected adults, 315 identified themselves as Latinos, 323 identified themselves as blacks, 254 identified themselves as Asians, and 779 identified themselves as whites. In this survey, 86% of blacks said that their families would welcome a white person into their families. NOTE: If you are using a Student's t-distribution, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) Part (a) We are interested in finding the 95% confidence interval for the percent of all black adults who would welcome a white person into their families. In words, define the random variables $X$ and $P$. $X$ is the proportion of families that approve of interracial dating and marriage, and $P$ is the number of families that approve of interracial dating and marriage. $X$ is the proportion of black families that would welcome a white person into their family, and $P$ is the number of black families that would welcome a white person into their family. $X$ is the number of families that approve of interracial dating and marriage, and $P$ is the proportion of families that approve of interracial dating and marriage. $X$ is the number of black families that would welcome a white person into their family and $P$ is the proportion of black families that would welcome a white person into their family.

Transcript

00:01 All right, we start out this problem with a lot of information.

00:04 We talk about the fact that we are dealing with a survey involving 1 ,709 adults.

00:12 And of those 179, it's broken up into latino, where there's 315, black, where there's 323, asian, where there's 254, and white, where there's 254, and white, where there's, there was 779 people.

00:45 And this particular problem is having us focus in on the black subcategory.

00:54 So going forward in this problem, our n value is going to be 323.

01:01 The first part of this problem, part a, is asking you to define the variable x.

01:10 And since we are interested in finding a confidence interval for the percent of all black adults who would welcome a white person, then the x represents the number of black adults who say their families would welcome a white person into their families.

02:03 And the p prime in this problem represents the proportion of black adults in this sample who say their families would welcome.

02:43 A white person into their families.

03:05 So as we go into part b, we have to again think about how many people are in this survey and how many, what percentage or what proportion are favorable.

03:23 So in part b, it's asking us what type of distribution would we use to solve? and we're going to use the normal distribution because we know that the sample size was 323 black adults that were asked, and the p prime was that 86 % would welcome white into their family.

03:59 So when we use our normal distribution, we're using normal distributions because the sample size is large and p prime is not close to 0 or 1.

04:31 And the notation that's going to go with this is going to be n for normal, the p prime, and then the square root of p prime, q prime, all over the sample size.

04:47 So with our numbers associated with this problem, it's going to be 0 .86, comma, the square root of 0 .86 for p prime, q prime is going to be 0 .14 because p prime plus q prime has to add up to 1, and our n value is 323.

05:13 So we are ready to tackle a 95 % confidence interval in part c.

05:23 So in part c, we're trying to find the confidence interval at the 95 % level.

05:34 And in order to do that, we're going to have to find the error bound first.

05:40 And that is technically part three of part c.

05:43 So to do part three of part c, we're going to do the error bound of the proportion equals z of alpha sub -alpha over two multiplied by the square root of p prime, q -prime, all over now, in order to find that z score that we need for that formula, i like you to think of your bell -shaped curve, the standard normal curve.

06:16 And if we're doing a 95 % confidence interval, then we are talking about the 95 % in the center of that bell -shaped curve.

06:24 That means there's 5 % of the curve left that we have unaccounted for.

06:31 And when we take that 5 % and we see that 5 % and we split it in two, we will have 0 .025 or 2 .5 % in each of the two tails.

06:43 So we'll have 025 over in this tail, and we'll have 0 .025 over in this tail.

06:50 So for us to calculate the z associated with each of those boundaries, the lower boundary and the upper boundary of the confidence interval, we are going to have to use the inverse norm on our calculator.

07:06 So the z will be found by doing inverse norm, and then you'll have to insert the area in each tail, followed by the mean of the standard normal curve, and the standard deviation of the standard normal curve...

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