What is 2a+4b= and whats the equation
2 answers:
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Answer:
1. d. (0.652, 0.726)
2. b. (0.661, 0.718)
a. The margin of error of a 90% confidence interval will be less than the margin of error for the 95% and 99% confidence intervals because intervals get wider with increasing confidence level.
Step-by-step explanation:
Data given and notation
n=1023 represent the random sample taken in 2017
X=705 represent the people who thinks that believe that marijuana should be legalized.
estimated proportion of people who thinks that believe that marijuana should be legalized.
z would represent the statistic in order to find the confidence interval
p= population proportion of people who thinks that believe that marijuana should be legalized.
Part 1
The confidence interval would be given by this formula
For the 99% confidence interval the value of and
, with that value we can find the quantile required for the interval in the normal standard distribution.
And replacing into the confidence interval formula we got:
0.689 -2.58 sqrt((0.689(1-0.689))/(1023))=0.652
0.689 + 2.58sqrt((0.56(1-0.689))/{1023))=0.726
And the 99% confidence interval would be given (0.652;0.726).
We are 99% confident that about 65.2% to 72.6% of people believe that marijuana should be legalized
d. (0.652, 0.726)
Part 2
The confidence interval would be given by this formula
For the 95% confidence interval the value of and
, with that value we can find the quantile required for the interval in the normal standard distribution.
And replacing into the confidence interval formula we got:
0.689 - 1.96((0.689(1-0.689))/(1023))=0.661
0.689 + 1.96 ((frac{0.56(1-0.689))/(1023))=0.718
And the 95% confidence interval would be given (0.661;0.718).
We are 95% confident that about 66.1% to 71.8% of people believe that marijuana should be legalized
b. (0.661, 0.718)
Part 3
Would be lower since the quantile for a lower confidence is lower than a quantile for a higher confidence level.
The margin of error of a 90% confidence interval will be less than the margin of error for the 95% and 99% confidence intervals
If we calculate the 90% interval we got:
For the 90% confidence interval the value of and
, with that value we can find the quantile required for the interval in the normal standard distribution. The quantile for this case would be 1.64.
And replacing into the confidence interval formula we got:
0.689 - 1.64 ((0.689(1-0.689))/{1023))=0.665
0.689 + 1.64 ((0.56(1-0.689))/(1023))=0.713
And the 90% confidence interval would be given (0.665;0.713).
We are 90% confident that about 66.5% to 71.3% of people believe that marijuana should be legalized.
The intervals get wider with increasing confidence level.
So the correct answer is:
a. The margin of error of a 90% confidence interval will be less than the margin of error for the 95% and 99% confidence intervals because intervals get wider with increasing confidence level.
Answer:
The box-and-whisker plot of this distribution is presented in the attached image to this solution.
Step-by-step explanation:
A box plot gives a visual representation of the distribution of the data, showing where most values lie and those values that greatly differ from the rest, called outliers.
A box and whiskers plot shows 5 major information about the distribution of data. It shows:
- The maximum variable.
- The minimum variable.
- The Median.
- The first quartile.
- The third quartile.
Further info such as the range and Inter quartile range can then be obtained from this 5-number summary.
The elements of the box plot are described thus;
The bottom side of the box represents the first quartile, and the top side, the third quartile. Therefore, the width of the central box represents the inter-quartile range.
The horizontal line inside the box is the median.
The lines extending from the box reach out to the minimum and the maximum values in the data set, as long as these values are not outliers. The ends of the whiskers are marked by two shorter horizontal lines.
Variables in the dataset, higher than Q3+(1.5×IQR) or lower than Q1-(1.5×IQR) are considered outliers and are usually shown using dots above the top whisker or below the bottom whisker.
The required boxplot for this question is given in the attached image to this solution.
The median for the boxplot isn't provided, but it was assumed to be midway between the first and third quartile.
Hope this Helps!!!
