Mathematics, 19.12.2019 02:31 3mory2006p78jan

Asurvey of 2280 adults in a certain large country aged 18 and older conducted by reputable polling organization founded that 424 have donated blood in the past two years. complete parts (a) through (c).a) obtain a point estimate for the population proportion of adults in the country age 18 and older who have donated blood in the past two years. b) verify that the requirements for constructing a confidence interval. the sample [ a) can be assumed to be b)is stated to not be. c) cannot be assumed to be. d) is stated to be. ] a simple random sample, the value of [ a)np b) p(1-p) c) np(1-p) d) p.] is [ ]. which is [ a) greater than. b) less then] 10. & the [ a) population size b) sample population c) sample size d) population proportion] [ a)can be assumed to be. b) is stated to not be c) cannot be assumed to be d) is stated to] less than or equal to 5% of the [a) sample proportion b) population proportion c) population size d) sample size.]c. construct and interpret a 90% confidence interval for the population proportion of adults in the country who have donated blood in the past two years. select the correct choice below and fill in any answer box within your choice.( type integer or decimal rounded to three decimal places as needed. use ascending order)a) we are [ ]% confident the proportion of adults in the country aged 18 and older who have donated blood in the past two years is between [ ] and [ ].
b) there is a [ ]% chance the proportion of adults in the country aged 18 and older who have donated blood in the past 2 years is between [ ] and [ ].

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Answer from: daedae11142

a) $\hat p=\frac{424}{2280}=0.186$ estimated proportion of people that donated blood in the past two years

b) i)The random sample needs to be representative: On this case the problem no mention about it but we can assume it.

ii) The sample needs to be large enough

np_o =2280*0.186=424.0810

n(1-p_o)=2280*(1-0.186)=319.210

c) The 90% confidence interval would be given (0.173;0.199).

A) we are [90 ]% confident the proportion of adults in the country aged 18 and older who have donated blood in the past two years is between [0.173 ] and [0.199 ]

Step-by-step explanation:

1) Data given and notation

n=2280 represent the random sample taken

X=424 represent the people that donated blood in the past two years

$\hat p=\frac{424}{2280}=0.186$ estimated proportion of people that donated blood in the past two years

$\alpha=0.05$ represent the significance level (no given, but is assumed)

z would represent the statistic (variable of interest)

p_v represent the p value (variable of interest)

p= population proportion of people that donated blood in the past two years

a) obtain a point estimate for the population proportion of adults in the country age 18 and older who have donated blood in the past two years.

$\hat p=\frac{424}{2280}=0.186$ estimated proportion of people that donated blood in the past two years

b) verify that the requirements for constructing a confidence interval.the sample

Check for the assumptions that he sample must satisfy in order to use the confidence interval

i)The random sample needs to be representative: On this case the problem no mention about it but we can assume it.

ii) The sample needs to be large enough

np_o =2280*0.186=424.0810

n(1-p_o)=2280*(1-0.186)=319.210

c. construct and interpret a 90% confidence interval for the population proportion of adults in the country who have donated blood in the past two years.

The confidence interval would be given by this formula

$\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

For the 90% confidence interval the value of $\alpha=1-0.9=0.1$ and $\alpha/2=0.05$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=1.64$

And replacing into the confidence interval formula we got:

$0.186 - 1.64 \sqrt{\frac{0.186(1-0.186)}{2280}}=0.173$

$0.186 + 1.64 \sqrt{\frac{0.186(1-0.186)}{2280}}=0.199$

And the 90% confidence interval would be given (0.173;0.199).

A) we are [90 ]% confident the proportion of adults in the country aged 18 and older who have donated blood in the past two years is between [0.173 ] and [0.199 ]

Answer from: Quest

the range of a function is the range of y-values for which it is defined, or exists. given that we are only looking at the y-values, we can already discount the first two answers as they deal with the domain of the function (range of x-values).

now, what we need to do is find the smallest and highest y-values for which the function is defined. if you'd like, you could take a ruler and start at the very bottom of the graph, find the lowest point, then move the ruler higher and higher until you reach the highest point. doing so either in your head or with an actual ruler, we can see that the lowest y-value is -5 and the highest y-value is -1.

the question now remains as to whether they are included in the range (fourth answer) or excluded (third answer). the key here is to recognise whether they are marked with an open or a closed circle. since both (-2, -5) and (2, -1) are marked with a closed circle, they are points that exist on the graph and are thus included in the range (note that if they were marked with an open circle like (4, -2) then that would signify that there is a break in the graph at that point).

thus, the fourth answer, (y | -5 ≤ y ≤ -1), is correct.

also note that usually it is good practice to scan your eye inbetween the highest and lowest point for any breaks in the graph - we do have one here at (4, -2), however -2 is still included in the range because there is another point that is included in the graph with the same y-value, ie. point (1, -2).

i hope that but if you require any further explanation don't hesitate to comment below.